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1. Finite Difference Methods for
2. The Finite Difference Time Domain
3. Finite Difference Schemes and
4. Schaum's Outline of Calculus of
5. Finite Difference Equations
6. Finite-Difference Methods for
7. Calculus of Finite Differences
8. Calculus of Finite Differences
9. Calculus of Finite Differences
10. Pricing Financial Instruments:
11. Computational Electrodynamics:
12. The Finite Difference Method in
13. Numerical Solution of Partial
14. Finite Difference Time Domain
15. Generalized Difference Methods
16. Introduction to Groundwater Modeling:
17. Theory & Problems of Finite
18. Numerical Partial Differential
19. Parallel Finite-Difference Time-Domain
20. Nonlinear Stability of Finite

1. Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems (Classics in Applied Mathematics)
by Randall Leveque
Paperback: 357 Pages (2007-07-10)
list price: US$63.00 -- used & new: US$52.00
(price subject to change: see help)
Asin: 0898716292
Average Customer Review: 5.0 out of 5 stars
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Editorial Review

Product Description
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.

The book is organized into two main sections and a set of appendices. Part I addresses steady-state boundary value problems, starting with two-point boundary value problems in one dimension, followed by coverage of elliptic problems in two and three dimensions. It concludes with a chapter on iterative methods for large sparse linear systems that emphasizes systems arising from difference approximations. Part II addresses time-dependent problems, starting with the initial value problem for ODEs, moving on to initial boundary value problems for parabolic and hyperbolic PDEs, and concluding with a chapter on mixed equations combining features of ODEs, parabolic equations, and hyperbolic equations. The appendices cover concepts pertinent to Parts I and II. Exercises and student projects, developed in conjunction with this book, are available on the book s webpage along with numerous MATLAB m-files.

Readers will gain an understanding of the essential ideas that underlie the development, analysis, and practical use of finite difference methods as well as the key concepts of stability theory, their relation to one another, and their practical implications. The author provides a foundation from which students can approach more advanced topics and further explore the theory and/or use of finite difference methods according to their interests and needs.

Audience: This book is designed as an introductory graduate-level textbook on finite difference methods and their analysis. It is also appropriate for researchers who desire an introduction to the use of these methods.

Contents: Preface; Part I: Boundary Value Problems and Iterative Methods. Chapter 1: Finite Difference Approximations; Chapter 2: Steady States and Boundary Value Problems; Chapter 3: Elliptic Equations; Chapter 4: Iterative Methods for Sparse Linear Systems; Part II: Initial Value Problems. Chapter 5: The Initial Value Problem for Ordinary Differential Equations; Chapter 6: Zero-Stability and Convergence for Initial Value Problems; Chapter 7: Absolute Stability for Ordinary Differential Equations; Chapter 8: Stiff Ordinary Differential Equations; Chapter 9: Diffusion Equations and Parabolic Problems; Chapter 10: Advection Equations and Hyperbolic Systems; Chapter 11: Mixed Equations; Appendix A: Measuring Errors; Appendix B: Polynomial Interpolation and Orthogonal Polynomials; Appendix C: Eigenvalues and Inner-Product Norms; Appendix D: Matrix Powers and Exponentials; Appendix E: Partial Differential Equations; Bibliography; Index. ... Read more

Customer Reviews (1)

5-0 out of 5 stars Good book
This is a great book for numerical analysis and finite differences. The author makes it simple to understand(well mostly) without sacrificing rigor.
... Read more

2. The Finite Difference Time Domain Method for Electromagnetics: With MATLAB Simulations
by Atef Elsherbeni, Veysel Demir
Hardcover: 450 Pages (2009-01-02)
list price: US$129.00 -- used & new: US$105.00
(price subject to change: see help)
Asin: 1891121715
Average Customer Review: 4.5 out of 5 stars
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Editorial Review

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The scope of the book is the fundamental techniques in the FDTD method. The book consists of 12 chapters, each chapter built on the concepts provided in the previous chapters. In each chapter, the details of the concepts are discussed at a graduate student level. Using this book, students will be able to construct a program with sufficient functionally to solve some basic problems. The construction of final equations is presented with a detailed step-by-step approach. In most cases the full-set of equations are provided.

While constructing the equations, the reader needs to visualize the positioning and orientation of field components in a three dimensional space. This is very difficult and usually requires extensive experience to be able to imagine the 3D space. Therefore, the book presents the construction of equations accompanied by a nice set of 3D illustrations. The figures greatly facilitate the understanding of the concepts.

While the concepts are being presented, it has been kept in mind that the outcome of the book will be a software package that will be sufficient to solve several types of basic electromagnetic problems. In each chapter the transformation of the concepts into programming is explained. Therefore the chapters are presented in such a way that, by adding/developing a new part of the code, chapter by chapter, at the end a well developed FDTD simulation package will be constructed. This book provides full derivations for final equations. It contains 3-D illustrations to aid in visualization of field components. Detailed explanations take the reader from conceptual understanding to actual program development. The book offers step-by-step construction of a basic FDTD simulation package. Fully functional code examples are also provided. ... Read more

Customer Reviews (3)

3-0 out of 5 stars A puzzle of m files
I am interesting in scattering. I went directly to chapter 11. Chapter is easy to follow. explains a bunch of m files. I took a look to the cd with the code. Several m files are sit in the directory chapter_11 and there are 3 subdirectories with examples. The directories with examples are missing several m files that I am guessing are spread around the other directories corresponding to other chapters. No user guide about which files you need or order to run them. I tried and start getting errors and errors of missing variables and m files. Files such as initialize_waveform. I found this particular m file in directories of other chapters. I figured it out and run it but surprise, now I was missing a variable c(speed of light). Could not find which m file it is defined. I did myself but more and more missing variables start showing up... The authors should have put all the files you need to run the examples in their own directories. My guess is that one cannot jump directly to a particular chapter and must follow the chapters in sequence... Summarizing: I could not run any of the examples in chapter 11 out of the cd

5-0 out of 5 stars Good stuff.
Taflove's book is the standard 'bible' on FDTD. It is the one to go to for the theory and cutting research applications.
--But this book is a wonderful companion! ...becuase it is focused on how to write your own FDTD codes in MATLAB step-by-step, and illuminates many pitfalls most beginners encounter and subtle points not touched on elsewhere. Very well-put together text. Even serves as a general MATLAB learning text.

5-0 out of 5 stars Excellent book on FDTD implementation
This book is an excellent book for whomever is interested in building his/her own FDTD code. It uses MATLAB as the basis for programming, but since the coding style is written so clearly, it should be easy to convert to any other language when so desired.

More importantly (for me at least), I had been struggling with getting accurate results from commercial FDTD programs. Reading this book has helped me get a solid understanding of the underlying mechanisms of FDTD, which in turn has helped me setup simulation models in FDTD that run accurately without incurring too much additional simulation time overhead.

I'd highly recommend this book to anyone who is interested in, or is working with, FDTD. This book focuses mostly on the practical implementation and use of FDTD. For a more fundamental approach, I'd recommend Taflove's book, in addition to this one. ... Read more

3. Finite Difference Schemes and Partial Differential Equations
by John Strikwerda
Paperback: 450 Pages (2007-10-31)
list price: US$112.50 -- used & new: US$119.44
(price subject to change: see help)
Asin: 089871639X
Average Customer Review: 5.0 out of 5 stars
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Editorial Review

Product Description
This book provides a unified and accessible introduction to the basic theory of finite difference schemes applied to the numerical solution of partial differential equations. Originally published in 1989, its objective remains to clearly present the basic methods necessary to perform finite difference schemes and to understand the theory underlying these schemes. This is one of the few texts in the field to not only present the theory of stability in a rigorous and clear manner but also to discuss the theory of initial-boundary value problems in relation to finite difference schemes. In this updated edition the notion of a stability domain is now included in the definition of stability and is more prevalent throughout the book. The author has also added many new figures and tables to clarify important concepts and illustrate the properties of finite difference schemes. ... Read more

Customer Reviews (2)

5-0 out of 5 stars Math Student
The book was in perfect condition for a great price.Exactly what I expected.

5-0 out of 5 stars One of the best books ever
This book deals with the broad range of PDE problems with wonderful numerical algorithms.
I was crushed on the 1st edition because it was really well-balanced(i.e.,just necessary math but full coverage of real world interests) and well-organized book.
This book (the 2nd edition) includes more pictures and examples which help the reader to undersand the important concepts with ease.
Sometimes, the brief sentences seem to be too concise to the fist reader, but that is not true.
Once the reader understand the previous stuff, he or she does not need to look other books to understand the next stuff.
(Of cousre, this claim might not be applied to undergrads, because this book is inteneded to the first year grads. See preface.)
This book can be used as a text book in math or computer science class, but to engineers like me, this book is amzing even to the researchers who are closely got involved with physical modeling or simulation.

It is very difficult to meet good people, and it seems to be lucky if we meet those kinds of people.
This is also true for us to meet well-written books.
I feel I am very lucky to find this book.

... Read more

4. Schaum's Outline of Calculus of Finite Differences and Difference Equations
by Murray Spiegel
Paperback: 272 Pages (1971-12-01)
list price: US$19.95 -- used & new: US$8.99
(price subject to change: see help)
Asin: 0070602182
Average Customer Review: 4.0 out of 5 stars
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Editorial Review

Product Description
This powerful study tool covers difference calculus, sum calculus, ifference equations and more with many examples of their applications. Ideal for solo study or as a supplement to a course, it clearly explains principles and theorems and gives definitions, then takes students through problems and their step-by-step solutions. This provides firm footing and excellent preparation for real-life problems and school examinations. ... Read more

Customer Reviews (2)

5-0 out of 5 stars One of the best books, not just outline books
This is supposedly a review book. Yet I think it is one of the best books on the subject. It is elementary, and might not cover all the latest advances, yet it has a wealth of examples, beautiful explanations, and a very nice assortment of subjects. I particularly liked his lozenge diagram approach to methods of integration, his concise and lucid explanation of the Euler-Maclaurin sum formula, applications of the sum calculus, and clear parallels to standard calculus (ininitesimal) throughout. You can't do much better than this well-written text for basics of finite differences.

3-0 out of 5 stars Handy, but not perfect
This book discusses difference calculus, sum calculus, and difference equations as well as discusses applications.With each chapter, there are plenty of explanations and examples.The book also has problems you can try to test your knowledge of the chapter.

The problem I have with it is that not all the problems have answers to them.The explanations are great, but I want to make sure I understand it.There doesn't seem to be a pattern regarding which ones have answers in the back.You just have to try the problem, then look in the back to see if that one was answered.

I would still recommend this to help reinforce what you learn in class or just to refresh your memory. ... Read more

5. Finite Difference Equations
by H. Levy, F. Lessman
Paperback: 278 Pages (1992-09-11)
list price: US$12.95
Isbn: 0486672603
Average Customer Review: 4.5 out of 5 stars
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Product Description
Comprehensive study focuses on use of calculus of finite differences as an approximation method for solving troublesome differential equations. Elementary difference operations; interpolation and extrapolation; modes of expansion of the solutions of nonlinear equations, applications of difference equations, difference equations associated with functions of two variables, more. Exercises with answers. 1961 edition.
... Read more

Customer Reviews (2)

5-0 out of 5 stars Clear introduction and very useful exercises
As offered on the back cover, stress is on problem solving and not on pure mathematics.However, this does not mean that the treatment is informal.The language is precise and the concepts are clearly defined.The exercises are useful and range from very easy to somewhat challenging.Preliminaries have been kept to a minimum and people who have taken their Calculus and Linear Algebra should have no problems working their way through this book.

4-0 out of 5 stars Interesting
Very good book on how to use finite difference equations. ... Read more

6. Finite-Difference Methods for Partial Differential Equations (DoverPhoenix Editions)
by George E. Forsythe, Wolfgang R. Wasow
Hardcover: 464 Pages (2004-11-23)
list price: US$75.00 -- used & new: US$24.00
(price subject to change: see help)
Asin: 0486439178
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An interrelated account of many of the most important finite difference methods and their results, this text is geared toward upper-level undergraduates and graduate students. Topics include hyperbolic equations in two independent variables, parabolic and elliptic equations, and initial-value problems in more than two independent variables. 1960 edition.
... Read more

7. Calculus of Finite Differences (Classic Reprint)
by George Boole
Paperback: 364 Pages (2010-03-23)
list price: US$10.37 -- used & new: US$10.37
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Asin: 1440059004
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( 4 ) CHAPTER II. direct theorems of finite differences. 1. The operation denoted by A is capable of repetition. For the difference of a function of x, being itself a function of x, is subject to operations of the same kind. In accordance with the algebraic notation of indices, the difference of the difference of a function of x, usually called the second difference, is expressed by attaching the index 2 to the symbol A. Thus AAws= AX- In like manner AAX = AX, and generally AA"~X = AX (1), the last member being termed the nth difference of the function ux. If we suppose ux = »3, the successive values of ux with their successive differences of the first, second, and third orders will be represented in the following scheme: Values of X 1 2 3 4 5 6 . 1 8 27 64 125 216 At*. 7 19 37 61 91 ... AX 12 18 24 30... AX 6 6 6... It may be observed that each set of differences may either be formed from the preceding set by successive subtractions in accordance with the

Table of Contents

CONTENTS; DIFFERENCE- AND SUM-CALCULUS CHAPTER I; pagk; NATURE OF THE CALCULUS OF FINITE DIFFERENCES 1; CHAPTER II; DIRECT THEOREMS OF FINITE DIFFERENCES 4; Differences of Elementary Functions, 6 Expansion in factorials, 11; Generating Functions, 14 Laws and relations of E, A and j^, 16; Secondary form of Maclaurin's Theorem, 22 HerBchePs Theo-rem, 24 Miscellaneous Expansions, 25 Exercises, 28; CHAPTER III; ON INTERPOLATION, AND MECHANICAL QUADRATURE 33; Nature of the Problem, 33 Given values equidistant, 34 Not equidistant-Lagrange's Method, 38 Gauss' Method, 42 Cauchy's Method, 43 Application to Statistics, 43 Areas of Curves, 46 Weddle's rule, 48 Gauss' Theorem on the best position of the given ordinates, 51 Laplace's method of Quadratures, 53 References on Interpolation, &c 55 Connexion between Gauss' Theorem and Laplace's Coefficients, 57 Exercises, 57 B F D b; X; CONTENTS; CHAPTER IV page; FINITE INTEGRATION, AND THE SUMMATION O ... Read more

8. Calculus of Finite Differences (AMS Chelsea Publishing)
by Charles Jordan
Hardcover: 654 Pages (1965-01-01)
list price: US$55.00 -- used & new: US$54.99
(price subject to change: see help)
Asin: 0828400334
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9. Calculus of Finite Differences Edition
by Louis Melville Milne-Thomson
 Hardcover: 558 Pages (1980-12)
list price: US$29.50
Isbn: 0828403082
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From the Preface: "The object of this book is to provide a simple and connected account of the subject of Finite Differences and to present the theory in a form which can be readily applied ... not only the useful material of Boole ... but also the more modern developments of the finite calculus ... [T]he book is suitable for a first course as well as for more advanced reading ... Operational and symbolic methods have been freely used throughout the book" ... Read more

10. Pricing Financial Instruments: The Finite Difference Method
by Domingo Tavella, Curt Randall
Hardcover: 237 Pages (2000-04-15)
list price: US$110.00 -- used & new: US$66.54
(price subject to change: see help)
Asin: 0471197602
Average Customer Review: 4.0 out of 5 stars
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Editorial Review

Product Description
Numerical methods for the solution of financial instrument pricing equations are fast becoming essential for practitioners of modern quantitative finance. Among the most promising of these new computational finance techniques is the finite difference method-yet, to date, no single resource has presented a quality, comprehensive overview of this revolutionary quantitative approach to risk management.

Pricing Financial Instruments, researched and written by Domingo Tavella and Curt Randall, two of the chief proponents of the finite difference method, presents a logical framework for applying the method of finite difference to the pricing of financial derivatives. Detailing the algorithmic and numerical procedures that are the foundation of both modern mathematical finance and the creation of financial products-while purposely keeping mathematical complexity to a minimum-this long-awaited book demonstrates how the techniques described can be used to accurately price simple and complex derivative structures.

From a summary of stochastic pricing processes and arbitrage pricing arguments, through the analysis of numerical schemes and the implications of discretization-and ending with case studies that are simple yet detailed enough to demonstrate the capabilities of the methodology- Pricing Financial Instruments explores areas that include:
* Pricing equations and the relationship be-tween European and American derivatives
* Detailed analyses of different stability analysis approaches
* Continuous and discrete sampling models for path dependent options
* One-dimensional and multi-dimensional coordinate transformations
* Numerical examples of barrier options, Asian options, forward swaps, and more

With an emphasis on how numerical solutions work and how the approximations involved affect the accuracy of the solutions, Pricing Financial Instruments takes us through doors opened wide by Black, Scholes, and Merton-and the arbitrage pricing principles they introduced in the early 1970s-to provide a step-by-step outline for sensibly interpreting the output of standard numerical schemes. It covers the understanding and application of today's finite difference method, and takes the reader to the next level of pricing financial instruments and managing financial risk.

Praise for Pricing Financial Instruments

"Pricing Financial Instruments is the first broad and accessible treatment of finite difference methods for pricing derivative securities. The authors have taken great care to clearly explain both the origins of the pricing problems in a financial setting, as well as many practical aspects of their numerical methods. The book covers a wide variety of applications, such as American options and credit derivatives. Both financial analysts and academic asset-pricing specialists will want to own a copy."-Darrell Duffie, Professor of Finance Stanford University

"In my experience, finite difference methods have proven to be a simple yet powerful tool for numerically solving the evolutionary PDEs that arise in modern mathematical finance. This book should finally dispel the widely held notion that these methods are somehow difficult or abstract. I highly recommend it to anyone interested in the implementation of these methods in the financial arena."-Peter Carr, Principal Bank of America Securities

"A very comprehensive treatment of the application of finite difference techniques to derivatives finance. Practitioners will find the many extensive examples very valuable and students will appreciate the rigorous attention paid to the many subtleties of finite difference techniques."-Francis Longstaff, Professor The Anderson School at UCLA

"The finite difference approach is central to the numerical pricing of financial securities. This book gives a clear and succinct introduction to this important subject. Highly recommended."-Mark Broadie, Associate Professor School of Business, Columbia University

For updates on new and bestselling Wiley Finance books: wiley.com/wbns ... Read more

Customer Reviews (5)

4-0 out of 5 stars Financial Engineering Review
It is a very good book, well written and didactic. It covers important topics related to Financial Engineering, such as Stochastic Processes, the Pricing Equations, it also covers numerical methods such as the Finite Difference Methods.There is a topic covering the linear complementarity formulation of American Option Pricing which was able to make me understand it much better than ever before.

3-0 out of 5 stars A specialised book for special Instruments
This book approximates the solution of one-factor and multi-factor PDEs that describe derivatives such as barrier options, convertible bonds, Asian options and credit derivatives.
Standard finite difference schemes are used. In particular, 3-point centred difference schemes approximate the derivatives in the S directions while Crank-Nicolson (averaging) is used to approximate the t derivative. Stability and convergence of the schemes are proved using the Lax Equivalence theoerem. Special attention is paid to resolving the, by now well known problems associated with the Crank Nicolson method. The workarounds are choosing smaller meshes near discontinuous boundaries, coordinate transformations and choosing the right sampling points.
The book is a good attempt (in my opinion) to show how to apply FDM in financial engineering applications. It is probably most useful for those who have already experience of FDM. It is NOT an introductory book.
Some of the criticisms are (this is why I give it a 3 star):

1. The von Neumann stability analyis technique is only applicable to constant coefficient, linear PDE. It is outdated, better methods being the maximum principle and viscosity solutions.

2. The discrete set of equations need to be solved by rather esoteric matrix solvers bacause the authors discretise a PDE in all directions. Using ADI or operator splitting instead lets us solve one-dimensional problem with Tridiagonal LU Decomposition.

3. A lot of detail on meshes has unfortunately been left out.

4. Using Crank Nicolson only aggrevates the problems in FDM schemes. There ARE better methods out there.

5. TYPOS!! for example, equation (4.13) on page 122. The S term is missing.

On the other hand, this book is aimed at real-life problems. However, extra detail needs to be added in my opinion in order to make it more accessible to a wider audience.

3-0 out of 5 stars Excellent Content - Sloppy Editing
Reading this book produced three instances where previously encountered material was explained from a new and different point of view, the clouds parted, and I was bathed in the bright sunshine of understanding.Creation and valuation of hedging portfolios, reduced to their fundamentals, is now far less taxing to the memory.Explanations for the discretization of time and space now render previously mysterious numerical algorithms obvious in their intent.American options discused in a free boundry framework are far more intuitive than in the optimal stoping time approach.As much as I enjoyed the content,the occurence of numerous editing oversights was a considerable annoyance.This was even more surprising when I read the other customer review which indicated that one of the authors was an editor.Editors should be held to a higher standard and so I deducted an extra star!

5-0 out of 5 stars A clear treatment, with well-chosen subjects
Tavella and Randall have produced a compact, yet complete treatment of finite difference techniques in finance.I met Curt Randall in 1996 when his SciFinance software was in its infancy (though there is currently no connection between us).This software automatically generates C code to solve PDE's.That is an order of magnitude -- maybe two orders -- harder than just writing the code by hand.I inferred that Dr. Randall has a unique understanding of finite-difference methods for solving PDE's.For these reasons, I was very interested to see his book.For a more general treatment finite difference schemes, see Gordon Smith's 1986 book.

The mathematical motivations for all the techniques presented are given, with no wasted exposition.I liked the lucid analyses of stability, which many books in finance gloss over.I also liked the mention and partial analysis of a large set of solvers of sparse linear systems.having not followed the literature on jump processes in recent years, I was quite happy to see their treatment as well.

This book is all of what it claims to be, and no more.I do not recommend it as a textbook, or as a reference for those not already somewhat familiar with the subject, either from the mathematics side or the finance side.You will not get an explanation of what an eigenvalue or fourier transform is.The Lax Equivalence Theorem is cited, but not motivated or proven.No mention is given of when it might make more sense to use, say, a Monte Carlo scheme to find an option price.You won't find much economics in the book.But you will find a clear, correct, and useful analysis of more or less all aspects of finite difference schemes as they relate to solving contingent claims pricing problems.

5-0 out of 5 stars A focussed book on an important subject
The pricing theory due to Black Scholes and Merton is widely recognized as one of the most significant contributions of economics to practice. There are now many good introductory books surveying the vast literature on the subject. So what is needed is a book showing how to implement variousmodels in practice. The book by Tavella and Randall is the first in what Ihope is a series of such books. The authors are well known in computationalcircles: Tavella is the editor of the highly regarded Journal ofComputational Finance and Randall is a Principal at SciComp, a leadingdeveloper of software synthesis technology for the finance industry. Theauthors focus on finite differences, which is an important generalizationof the common tree approach, and thus is one of the most widely usednumerical techniques in finance.

The book's first two chapters introducethe mathematics of financial derivatives in an intuitively appealingmanner.For example, measure changes are introduced as a powerful toolwithout strong demands on the reader in terms of background. Also, linearcomplementarity is used in the context of valuing American options, againin an intuitive fashion.The third chapter introduces finite differencesin the context ofthe familiar parabolic PDE governing derivative securityvalues. It is in this and the remaining chapters that much useful materialcan be found. For example, the cell averaging technique in chapter 4 is avery useful device for dampening the error introduced by slopediscontinuities which commonly occur in financial problems. The authorsalso give the first textbook treatment of the important class of pure jumpmodels such as the variance gamma model, which are growing in popularity.The chapter on coordinate transformations gives the finite differenceversion of what some finance people term the adaptive mesh method.

Insummary, this book is a must-read for anyone seriously interested inimplementing derivative security pricing models. I hope the authors plan tofollow up with a more advanced version which can cover such interestingtopics as multi-grid,hopskotch, operator splitting, and the like. ... Read more

11. Computational Electrodynamics: The Finite-Difference Time-Domain Method, Third Edition
by Allen Taflove, Susan C. Hagness
Hardcover: 1038 Pages (2005-06-30)
list price: US$159.00 -- used & new: US$141.78
(price subject to change: see help)
Asin: 1580538320
Average Customer Review: 5.0 out of 5 stars
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Product Description
This extensively revised and expanded third edition of the Artech House bestseller, Computational Electrodynamics: The Finite-Difference Time-Domain Method, offers you the most up-to-date and definitive resource on this critical method for solving Maxwell’s equations.There has been considerable advancement in FDTD computational technology over the past few years, and this new edition brings you the very latest details with four new invited chapters on advanced techniques for PSTD, unconditional stability, provably stable FDTD-FETD hybrids, and hardware acceleration. Moreover, you find many completely new sections throughout the book, including major updates on convolutional PML ABCs; dispersive, nonlinear, classical-gain, and quantum-gain materials; and micro-, nano-, and bio- photonics.

This single resource provides complete guidance on FDTD techniques and applications, from basic concepts, to the current state-of-the-art. It enables you to more efficiently and effectively design and analyze key electronics and photonics technologies, including wireless communications devices, high-speed digital and microwave circuits, and integrated optics. You find sample FDTD codes written in Matlab® that serve as a self-guided refresher, and examples of how to use the FDTD method on a wide range of projects in the field.What’s more, to supplement the third edition, the authors and publisher have created a Website where you can find solutions to the problems, sample FDTD PML codes, text updates/errata, and downloadable color graphics and videos. Consequently, this new edition is the ideal textbook for both a senior-year undergraduate elective course and a graduate course in computational electrodynamics. ... Read more

Customer Reviews (5)

4-0 out of 5 stars Excellent but a few topics have yet to be covered.
This is an excellent book that covers FDTD well but not completely.The authors are very knowledgeable and the book is quite easy to read.
A few things are not covered as well as I would have liked:
* Adding voltage, current sources.
* Adding resistors, inductors, caps.

Also, a few things such as the exponential equations for Berenger's PML are not covered well.To complement this, you need Berenger's original paper on the subject.

The example code on the web site for the publisher:
is exteremely useful, since the code contains what the text of the book is missing in cases.


I'd highly recommend this book as the foundational book for FDTD and also suggest that you complement this with some of the original papers and also the book:
The Finite-Difference Time-Domain Method for Electromagnetics with MATLAB simulations by Atef Elsherbeni and Veysel Demir,
which contains information on current,voltage sources and more extensive code examples.

5-0 out of 5 stars FDTD bible
This book has everything you need to know about FDTD. Dont waste your money on Sullivan's cook book. One minor problem in this book is the lack of examples (for example numerical validation) of code. EXCELLENT book.

5-0 out of 5 stars The book for FDTD
This book is an excellent and thoroughly enjoyable reference/tutorial. The book is suitable for use in an advanced undergraduate/first-year graduate class with a prerequisite of one semester of undergraduate E&M. (The authors' preface indicates that this prerequisite is not entirely necessary, but I don't see how you could understand what is going on without it.)

The book can also be used for self-study. In this vein, the book's website contains 1d-, 2d-, and 3d-matlab scripts that are excellent for learning how to actually implement all of this stuff. The third edition weighs in at just over 1000 pages with a price tag of $139, which is $10 cheaper than the 2nd edition was when it came out.

Allen Taflove is, perhaps, the leader in the development and use of this technique. Allen is now at Northwestern. Susan Hagness was a recent PhD student of his (1998) and is now an associateprofessor in the ElectricalandComputerEngineering department at theUniversityofWisconsin. The authors are at the forefront in the development of applications.

The third edition is significantly larger than the 2nd edition and includes several applications chapters that were cowritten with the major researchers in the field. The extraordinary explosion of application areas for FDTD is captured in the later chapters, and these chapters give students and new researchers a clear flavor of the vitality and interest in the field which extends from the detection of breast cancer to ELF pulses produced by earthquakes. It is refreshing to find authors who so readily give credit to others in their field. Taflove and Hagness have been very gracious in this regard, and as a consequence have a much better book and a very detailed and useful bibliography.

I very heartily recommend this book to anyone who wishes to use FDTD techniques.

5-0 out of 5 stars Agree with Prior Reviewer
I cannot quite honestly give this book (*first* edition, not second) a full five-point-zero stars because it somewhat comes apart the closer one gets to the final chapters.I read this book a few years ago, so I apologize for lack of specificity.However, Icompletely agree with the prior reviewer who stated that this book is better than Kunz's and Luebbers' book, which I appears to be a slightly edited compilation of previous publications --- even if that is completely untrue.In fact, in my opinion, Taflove's book (again, first edition) is a *much* better textbook than Kunz and Luebbers.

The Book News review is somewhat misleading.Taflove derives the difference equations in full, painstaking detail.(Perhaps the Book News reviewer fell asleep during that portion.)For me, this was the most valuable and educational portion of the book.Example applications have their place, but only after understanding the basic principles.Taflove did an excellent job in describing these principles, which go far beyond the basic Yee algorithm (e.g. extrapolation techniques and incorporation of BC's).Those readers familiar with other FD books should understand what I'm saying here: Anyone who reads this book and understands it will not only be conversant about FDTD but should also be able to write solid working codes.With the K&L book, this is very questionable.

5-0 out of 5 stars A good overview of FD-TD method
A good intro book for the FD-TD method with many applications. The list of references at the end of each chapter is also very useful. Some of the material is now outdated and needs corrections, but otherwise a greatreference for CEM. I would recommend this book over the Kunz & LuebbersFD-TD book. ... Read more

12. The Finite Difference Method in Partial Differential Equations
by Andrew R. Mitchell
 Hardcover: 284 Pages (1980-02)
list price: US$205.00 -- used & new: US$199.46
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Asin: 0471276413
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13. Numerical Solution of Partial Differential Equations: Finite Difference Methods (Oxford Applied Mathematics and Computing Science Series)
by G. D. Smith
Paperback: 350 Pages (1986-01-16)
list price: US$79.99 -- used & new: US$63.59
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Asin: 0198596502
Average Customer Review: 5.0 out of 5 stars
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Product Description
Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence.The new edition includes revised and greatly expanded sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods.A fast-paced introduction to numerical methods, this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline. ... Read more

Customer Reviews (1)

5-0 out of 5 stars Excellent introductory book on Finite Difference Method
I first used this book a long time ago (1988) when the third edition of it just came out, while I just got a chance to write a review on it much much years after that. It was a required graduate textbook at an Ivy League college. It discussed in depth the finite difference technique applied to the parabolic, elliptic, and hyperbolic types of PDEs. The thing that I really like about this book is, besides having not too much details on mathematical derivations, it gives examples on how to do the calculations by hand. Thus when one would like to "translate" all these calculations into a computer program one could easily test the results (or expected results). Of course there are a lot more books out there talking about finite difference technique but they are perhaps 20 bucks or more expensive than this book. The only minus about this book is it was printed in soft cover, even though mine is still in a very good condition after almost 16 years! I recommend this book for those beginners on finite difference method. I am currently using this book for one of my course. ... Read more

14. Finite Difference Time Domain Method for Electromagnetics
by Karl S. Kunz, Raymond J. Luebbers
Hardcover: 464 Pages (1993-07-03)
list price: US$136.95 -- used & new: US$208.95
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Asin: 0849386578
Average Customer Review: 5.0 out of 5 stars
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The Finite-Difference Time-domain (FDTD) method allows you to compute electromagnetic interaction for complex problem geometries with ease. The simplicity of the approach coupled with its far-reaching usefulness, create the powerful, popular method presented in The Finite Difference Time Domain Method for Electromagnetics. This volume offers timeless applications and formulations you can use to treat virtually any material type and geometry.The Finite Difference Time Domain Method for Electromagnetics explores the mathematical foundations of FDTD, including stability, outer radiation boundary conditions, and different coordinate systems. It covers derivations of FDTD for use with PEC, metal, lossy dielectrics, gyrotropic materials, and anisotropic materials. A number of applications are completely worked out with numerous figures to illustrate the results. It also includes a printed FORTRAN 77 version of the code that implements the technique in three dimensions for lossy dielectric materials. There are many methods for analyzing electromagnetic interactions for problem geometries. With The Finite Difference Time Domain Method for Electromagnetics, you will learn the simplest, most useful of these methods, from the basics through to the practical applications. ... Read more

Customer Reviews (1)

5-0 out of 5 stars The classics of FD-TD method
A good text for studying basics of FD-TD method for Electromagnetics.Especially, the chapters about surface impedance & dispersive materials were useful for me.But some misprint keep out of sight, you have to readcarefully. ... Read more

15. Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Volume Methods (Pure and Applied Mathematics)
by Ronghua Li, Zhongying Chen, Wei Wu
Hardcover: 472 Pages (2000-01-03)
list price: US$219.95 -- used & new: US$43.98
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Asin: 0824703308
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This text presents a comprehensive mathematical theory for elliptic, parabolic, and hyperbolic differential equations. It compares finite element and finite difference methods and illustrates applications of generalized difference methods to elastic bodies, electromagnetic fields, underground water pollution, and coupled sound-heat flows. ... Read more

16. Introduction to Groundwater Modeling: Finite Difference and Finite Element Methods
by Herbert F. Wang, Mary P. Anderson
Paperback: 237 Pages (1995-07-07)
list price: US$68.95
Isbn: 012734585X
Average Customer Review: 3.0 out of 5 stars
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The dramatic advances in the efficiency of digital computers during the past decade have provided hydrologists with a powerful tool for numerical modeling of groundwater systems. Introduction to Groundwater Modeling presents a broad, comprehensive overview of the fundamental concepts and applications of computerized groundwater modeling.
The book covers both finite difference and finite element methods and includes practical sample programs that demonstrate theoretical points described in the text. Each chapter is followed by problems, notes, and references to additional information. This volume will be indispensable to students in introductory groundwater modeling courses as well as to groundwater professionals wishing to gain a complete introduction to this vital subject.

Key Features
* Systematic exposition of the basic ideas and results of Hilbert space theory and functional analysis
* Great variety of applications that are not available in comparable books
* Different approach to the Lebesgue integral, which makes the theory easier, more intuitive, and more accessible to undergraduate students ... Read more

Customer Reviews (3)

4-0 out of 5 stars Introduction to Groundwater Modeling
I found this text very valuable in explaining the differences between these two methods and how each handles the dependent variable (head) and its first derivative (flow).The text also discusses Laplaces equation, iterative methods including Gauss-Seidel/SOR.Chapters are dedicated to finite difference and finite element methods under steady-state and transient conditions.It also demonstrates how each element is handled separately using finite element method and then the equations are assembled into a conductance matrix.

This text is a very good complement to other modeling texts.However, if you want to learn how to set up your hydrogeologic conceptual model, what data is needed to develop a good model, how to choose your numerical model, verify, calibrate your model, interpret results and perform a post audit, this is not that text.For the purpose of model setup etc. I would recommend Applied Groundwater Modeling.

1-0 out of 5 stars Outdated and of little value
I found this book somewhat outdated.Even though it was well-written if was of little value.There are several other books of better quality.

4-0 out of 5 stars Highly recommended
I've used this book in two of my groundwater modeling classes. Despite the fact that it is a little outdated, it has the clearest explaination I've come across of the mathematics behind groundwater modeling.In addition,it contains very good example problems. ... Read more

17. Theory & Problems of Finite Differences & Difference Equations,
by Murray R., Spiegel
 Paperback: Pages (1971)

Asin: B001D836V8
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18. Numerical Partial Differential Equations: Finite Difference Methods (Texts in Applied Mathematics)
by J.W. Thomas
Paperback: 460 Pages (2010-11-02)
list price: US$79.95 -- used & new: US$64.09
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Asin: 1441931058
Average Customer Review: 4.0 out of 5 stars
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What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.

... Read more

Customer Reviews (2)

4-0 out of 5 stars Good, practical book for FDM applied to PDE
This is a book that approximates the solution of parabolic, first order hyperbolic and systems of partial differential equations using standard finite difference schemes (FDM). The theory and practice of FDM is discussed in detail and numerous practical examples (heat equation, convection-diffusion) in one and two space variables are given. In particular, Alternating Direction Implicit (ADI) methods are the standard means of solving PDE in 2 and 3 dimensions.
In almost all cases model problems are taken in order to show how the schemes work for initial value problems, initial boundary value problem with Dirichlet and Neumann boundary conditions.
This book is a *must* for those in science, engineering and quantitative financial analysis. It digs into the nitty-gritty of mapping a PDE to a FDM scheme while taking nasty boundary conditions into consideration. The resulting algorithms are documented are are easily programmed in C++ or other language.
The book does not cover topics that are also important: operator splitting (Marchuk/Janenko), non-constant coefficient PDEs, nonlinearities. Finally, the book uses von Neumann analysis as a means of proving stability (getting a bit long in the tooth). There are more robust methods that use monotone schemes, M-matrices and the maximum principle. You should consult other specialised references.
This is Volume I of a two-volume set (Volume II deals with Conversation Laws and first-order hyperbolic as well as Elliptic problems.


4-0 out of 5 stars Numerical Partial Differential Equations
Thomas wrote a good book on a quite specialized subject.Although finite difference schemes have been traditionally viewed as a game field for physicists, they are given today much more commercial attention asfinancial option market evolves.Those who seek standard numerical recipesare advised to read this book.You will enjoy it (easy reading) and learn. But the book may not satisfy quests of a more rigorous readership.Itabuses the Fourier method in stability analysis while considering only PDEswith constant coefficients.The bibliographical work has not been done atall.In addition, the cover does not state that this is the first book oftwo.I'd also advise to read G.Marchuk "Methods of NumericalMathematics" (Springer, 1982) where a more general approach for stabilityof numerical schemes is developed. ... Read more

19. Parallel Finite-Difference Time-Domain Method (Artech House Electromagnetic Analysis)
by Wenhua Yu, Raj Mittra, Tao Su, Yongjun Liu, Xiaoling Yang
Hardcover: 274 Pages (2006-06-30)
list price: US$127.00 -- used & new: US$94.35
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Asin: 1596930853
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The finite-difference time-domain (FTDT) method has revolutionized antenna design and electromagnetics engineering. This book raises the FDTD method to the next level by empowering it with the vast capabilities of parallel computing. It shows engineers how to exploit the natural parallel properties of FDTD to improve the existing FDTD method and to efficiently solve more complex and large problem sets. Professionals learn how to apply open source software to develop parallel software and hardware to run FDTD in parallel for their projects. The book features hands-on examples that illustrate the power of parallel FDTD and presents practical strategies for carrying out parallel FDTD. This detailed resource provides instructions on downloading, installing, and setting up the required open source software on either Windows or Linux systems, and includes a handy tutorial on parallel programming. ... Read more

20. Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws: and Well-Balanced Schemes for Sources (Frontiers in Mathematics)
by François Bouchut
Paperback: 134 Pages (2005-03-23)
list price: US$49.95 -- used & new: US$34.93
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Asin: 3764366656
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Editorial Review

Product Description

This book is devoted to finite volume methods for hyperbolic systems of conservation laws. The accent is put on the development of tools for analyzing the nonlinear stability of Godunov schemes. Starting from theoretical considerations, the schemes are derived until a very practical level, meeting some required features such as for example the treatment of vacuum in gas dynamics. In the case of sources, the general notions of consistency, order of accuracy and well-balancing are developed, and applied to the construction of effective schemes.

... Read more

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