61. Comparison Of An Implicite Vs. Explicite One-dimensional Finite Differences Prog comparison of an implicit vs. explicit onedimensional finite differencesprogram for solving the unsteady heat-flow-equation. The http://www.geomath.onlinehome.de/models/implexpl.html

comparison of an implicit vs. explicit one-dimensional finite differences program for solving the unsteady heat-flow-equation The heat-flow equation (without source-term): The input data-file (identical for both programs) The explicit version (Fortran 77 source code) The implict version (Fortran 77 source code) A small programm for comparison of the results (Fortran 77 source code) The programs calculate the heat distribution at a 100m long row in one year, where the row has the following thermal properties: Heat conduction = 1.5 (W/(K m)) The time step is in both cases 1 hour Initial temperature = 283.15 K Spatial step size 1 m At the first 3 grid nodes there is a Dirichlet border condition with a T of 283.15 + 50 (K) The results: Explicit Implicit The difference (really small - only at the borders there is a bigger difference probably because of a malfunction of the SY-Subroutine): Author: , 28. May 2002

62. Atlas: Holistic Finite Differences Accurately Model The Dynamics Of The Kuramoto Holistic finite differences accurately model the dynamics of the KuramotoSivashinskyequation presented by Tony MacKenzie University of Southern Queensland http://atlas-conferences.com/c/a/d/r/29.htm

Atlas Document # cadr-29 Computational Techniques and Applications Conference and Workshops - CTAC99 September 20-24, 1999 The Australian National University Canberra, ACT, Australia Conference Organizers Mike Osborne, Bob Gingold, Steve Roberts, David Harrar II, Thanh Tran, Bob Anderssen, Henry Gardner, Markus Hegland and Lutz Grosz View Abstracts Conference Homepage Holistic finite differences accurately model the dynamics of the Kuramoto-Sivashinsky equation presented by Tony MacKenzie University of Southern Queensland joint research with Tony Roberts (University of Southern Queensland) We analyse the fourth order nonlinear Kuramoto-Sivashinsky equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately models the dynamics and may be constructed systematically. The theory is applied after dividing the physical domain into small elements by introducing insulating internal boundaries which are later removed. The Kuramoto-Sivashinsky equation is used as an example to show how holistic finite differences may be applied to fourth order nonlinear spatio-temporal dynamical systems. This novel centre manifold approach is holistic in the sense that it treats the dynamical equations as a whole, not just as the sum of separate terms. Date received: September 1, 1999

63. Calculus Of Finite Differences Top Level Subjects Science Mathematics Analysis Other analyticmethods Calculus of finite differences. Numerical differentiation; http://www.renardus.org/cgi-bin/genDDCbrowseSQL.pl?node=AATDG

64. Cell-centered Finite Differences http://www.ticam.utexas.edu/CSM/ACTI/DOE/sld020.htm

65. 2 FINITE DIFFERENCES previous up next contents index Previous INTRODUCTION Up CONTENTSNext 2.1 Explicit 2 levels. 2 finite differences. 2.1 Explicit http://pde.fusion.kth.se/SYL/sec2.php3

Previous: INTRODUCTION Up: CONTENTS Next: 2.1 Explicit 2 levels 2 FINITE DIFFERENCES 2.1 Explicit 2 levels 2.2 Explicit 3 levels 2.3 Lax-Wendroff 2.4 Leapfrog, staggered grid ... www.lifelong-learners.com

66. Numerical Analysis Lecture Slides On Finite Differences Engineering Mathematics 2 Numerical Analysis.Lecture slides on finite differences. http://www.enm.bris.ac.uk/anm/staff/rew/teaching/numanal/scan4.html

67. P-adic Analysis And The Calculus Of Finite Differences Padic analysis and the calculus of finite differences. L. Van Hamme Vrije UniversiteitBrussel Faculteit Toegepaste Wetenschappen Brussels, Belgium. Date http://www-math.sci.kun.nl/p-adic2002/abstracts/vanHamme/vanHamme.html

P-adic analysis and the calculus of finite differences L. Van Hamme Vrije Universiteit Brussel Faculteit Toegepaste Wetenschappen Brussels, Belgium Date: Abstract: It is well known that the role of the calculus of finite differences is much greater in p-adic analysis than in real or complex analysis. This paper confirms this once again. Our main result is a finite difference expansion for the derivative of an odd C function. The formula is fairly general since it depends on an arbitrary bounded sequence.

68. Ivo Oprsal's Finite Differences -diploma Thesis- Page For this thesis, please refer to Ivo Oprsal, 'ELASTIC FINITE DIFFERENCE SCHEMEFOR TOPOGRAPHY MODELS ON IRREGULAR GRIDS', Diploma Thesis, Dept. http://karel.troja.mff.cuni.cz/students/oprsal/geophys/diploma1996/dipl.htm

For this thesis, please refer to: Ivo Oprsal, ELASTIC FINITE DIFFERENCE SCHEME FOR TOPOGRAPHY MODELS ON IRREGULAR GRIDS' Diploma Thesis, Dept. of Geophysics, Charles University, Prague, May 1996. Here you can retreive the PDF version of camera ready copy (1.41 MB) (better for printing) , as it was defended at Dept. of Geophysics, Charles University, Prague, May 1996, and also winzipped Postscript version (818 kB). Click here to go back... Faculty of Mathematics and Physics Charles University in Prague ELASTIC FINITE DIFFERENCE SCHEME FOR TOPOGRAPHY MODELS ON IRREGULAR GRIDS Diploma Thesis Ivo Oprsal supervisor: Jiri Zahradnik Prague, May This research had been carried out at: Charles University, Faculty of Mathematics and Physics, Department of Geophysics, V Hole sovi ckách 2, 180 00 Praha 8, Czech Republic tel.: 42-2-8576 2546 fax.: 42-2-8576 2555 Email: io@karel.troja.mff.cuni.cz jz@karel.troja.mff.cuni.cz Contents ACKNOWLEDGEMENTS 1 INTRODUCTION 2 BASIC EQUATIONS 3 PSi-2 SCHEME FOR IRREGULAR GRID 3.1 Irregular grid

69. Ivo Oprsal - Finite Differences Compared To FE . The results of FDFE (finiteelement finite-differences) hybrid method of Moczoet al. (1997) for the ridge model were kindly provided by J. Kristek (Geophys. http://karel.troja.mff.cuni.cz/students/oprsal/geophys/fd_fdfe/fd_fdfe.htm

Comparison of FD and FDFE for topography model: model topography: Receivers R1 .. R13 are located on a free surface with a constant horizontal spacing of 166.66 m, the R1 receiver is on the top of the ridge. Receivers R14 .. R19 are located in depth z=615.6 m, the horizontal distance of these receivers is as follows: R14=0.0 m, R15=11.165 m, R16=166.667 m, R17=333.333 m, R18=500.0 m, R19=1000.0 m. There are no artificial reflections arriving to any of the receivers during the defined time window. Computation was done for a series of cases with v p =2000 m/s and v s =1400 , 1000 , 750 , 500 , 300 , 200 , 0.01 m/s (the last one being just formal). model 00 : v p =2000, v s =0.01 m/s, v p /v s = infinity ( formal ' liquid ridge ' ) model 01 : v p =2000, v s =200 m/s, v p /v s model 02 : v p =2000, v s =300 m/s, v p /v s model 03 : v p =2000, v s =500 m/s, v p /v s model 04 : v p =2000, v s =750 m/s, v p /v s model 05 : v p =2000, v s =1000 m/s, v p /v s model 06 : v p =2000, v s =1153 m/s, v p /v s = 1.73 ( =SQRT(3) ) model 07 : v p =2000, v s =1400 m/s, v p /v s = 1.42 ( This is just formal, not physical value of ratio ! ) The results of FDFE (finite-element finite-differences) hybrid method of Moczo et al. (1997) for the ridge model were kindly provided by J. Kristek (Geophys. Inst., Slovak Academy of Sciences, Bratislava, Slovakia).

70. Robotics Institute: Using Finite-Differences Methods For Approximating The Value First, we use a finite differences method for discretizing the HamiltonJacobi-Bellmanequation and obtain a finite Markovian Decision Process. http://www.ri.cmu.edu/pubs/pub_2946.html

RI Publications Text only version of this site Using Finite-Differences methods for approximating the value function of continuous Reinforcement Learning problems R. Munos International Symposium on Multi-Technology Information Processing 1996 Jump to: Download Abstract Notes Text Reference ... BibTeX Reference Download [ Help Adobe portable document format ( pdf ) [315 KB] Compressed postscript ( ps.gz ) [119 KB] Abstract This paper presents a reinforcement learning method for solving continuous optimal control problems when the dynamics of the system is unknown. First, we use a Finite Differences method for discretizing the Hamilton-Jacobi-Bellman equation and obtain a finite Markovian Decision Process. This permits us to approximate the value function of the continuous problem with piecewise constant functions defined on a grid. Then we propose to solve this MDP on-line with the available knowledge using a direct and convergent reinforcement learning algorithm, called the Finite-Differences Reinforcement Learning Notes Associated project: Auton Project Number of pages Text Reference R. Munos

71. Multiple Widths Yield Reliable Finite Differences (Computer Vision) April 1992 (Vol. 14, No. 4). pp. 412429 Multiple WidthsYield Reliable finite differences (Computer Vision). PDF. http://www.computer.org/tpami/tp1992/i0412abs.htm

April 1992 (Vol. 14, No. 4) p p. 412-429 Multiple Widths Yield Reliable Finite Differences (Computer Vision) M.M.  Fleck Index Terms- computer vision; integral equations; faint images; finite difference edge finder; low-amplitude responses; spurious responses; ideal straight step edge; Gaussian smoothing; spatial structure; noise; blurred features; computer vision; integral equations; noise The full text of IEEE Transactions on Pattern Analysis and Machine Intelligence is available to members of the IEEE Computer Society who have an online subscription and a web account

72. Use Of Finite Differences Home Course Home Page Up More on Bezier Curves The Use of FiniteDifferences. Producing many points on a curve or on a surface http://www.ece.eps.hw.ac.uk/~dml/cgonline/hyper00/curvesurf/findiff.html

73. Abstract Superconvergent Finite Differences I Superconvergent finite differences Applied to Transport Processes. byGF Carey and WF Spotz, 1992 Enhanced Oil and Gas Recovery Research http://www.scd.ucar.edu/css/staff/spotz/papers/EOGRR/abstract92.html

Superconvergent Finite Differences Applied to Transport Processes by G.F. Carey and W.F. Spotz, 1992 Enhanced Oil and Gas Recovery Research Annual Report, Austin, TX, April, 1992. Abstract A class of finite difference formulations which decrease the magnitude of the truncation error by using the governing differential equations to yield nodal superconvergence are developed. Typically, the increase is from O(h^2) to O(h^4) . This formulation is then applied to the convection diffusion problem for transport processes. An analytic model problem with known solution is studied and theoretical convergence rates are verified to be O(h^4) . Numerical experiments are conducted for representative example problems, which also show a suppresion of artificial oscillations commonly found in central differencing schemes. Back to Papers and Presentations Bill Spotz's Home Page Last updated February 24, 2000. Mail comments to Bill Spotz

74. Recent Contributions To The Calculus Of Finite Differences: A Survey Recent Contributions to the Calculus of finite differences A Survey.Reference Recent Contributions to the Calculus of finite differences http://dept-info.labri.u-bordeaux.fr/~loeb/cofd/a.html

Recent Contributions to the Calculus of Finite Differences: A Survey Reference: Recent Contributions to the Calculus of Finite Differences: A Survey, Lecture Notes in Pure and Applied Mathematics , Geometry and Complex Variables, editor: Salvatore Coen, Marcel Dekker 1991, 239276. with Gian-Carlo Rota. (Mathematical Review 93f:39013) Abstract: We retrace the recent history of the Umbral Calculus. After studying the classic results concerning polynomial sequences of binomial type, we generalize to a certain type of logarithmic series. Finally, we demonstrate numerous typical examples of our theory. Availability: This article is avaiable in: LaTeX source code Compressed source Postscript Compressed Postscript ... loeb@sprynet.com Last modified: Thu Nov 16 13:06:56 1995

75. CAU Kiel: Scattering States From Finite Differences Scattering states for realistic surfaces with multigrid acceleration.Fig. 1 Image of the charge density in the yz plane at x=0 http://www.theo-physik.uni-kiel.de/theo-physik/schattke/pres/mr97_c.html

Scattering states for realistic surfaces with multi-grid acceleration Fig. 1 As a first application a charge-density distribution of such a scattering state is shown in Fig. 1. The interface crystal vacuum, the decay of the wave function into the crystal, and the interference pattern of superimposed waves in the vacuum are clearly visible. The importance of the correct treatment of the potential barrier is illustrated by the strong charge fluctuations in the surface region. It is interesting to see that there are well localized regions of high charge density even at this nonbonding energy. See also: Calculation and physics of scattering states S. Lorenz, C. Solterbeck, W. Schattke, J. Burmeister, and W. Hackbusch, Electron scattering states at solid surfaces calculated with realistic potentials , Phys. Rev. B , 13432 (1997), also available as cond-mat/9702118 S. Lorenz, C. Solterbeck, O. Tiedje, W. Schattke, J. Burmeister, W. Hackbusch, Photoemission final states with realistic surface potentials /1997, p. 900 S. Lorenz

76. Results Similar pages PDF1 03P09 INTRODUCTION TO MODELLING LECTURE 1 - FINITE http://portal.acm.org/results.cfm?query=finite differences keyword&coll=por

77. MUG Convert Differential To Finite Differences (12.10.95) convert differential to finite differences (12.10.95). http://www-math.math.rwth-aachen.de/MapleAnswers/52.html

Maple User Group Answers [Anfang] [Hauptseite] [Suchen] ... [LDFM] convert differential to finite differences (12.10.95) Michel Carignan We have a testing lissence for Maple V Release 3. We want to know if some feature exist to convert the diff Maple operator involving in an expression with a custom one. We are interested in writing an expression involving partial differentials and then to convert all differential operator with the appropriate well know finite differences operator. Does Maple have a package to make finite difference algebra over fonctionel. If not, can you give us some hints to make one. Robert Israel It's quite easy using "subs". Something like this: Herbert Homeier t4720 A complete difference calculus would be very nice. I found the following procedure very useful to compute differences with regard to a global variable "n". (Obviously, one can make improve the procedure Delta to make checks of variable types, etc). It should also be possible to program a version where the difference is taken with respect to a variable chosen at will instead of the global "n". [Anfang] [Hauptseite] [Suchen] [LDFM] Dr. U. Klein

78. Finite Differences finite differences. The method of finite differences can sometimesbe used to guess a formula f(n) (but not to prove it). The way http://www.ms.uky.edu/~lee/ma310/tools/node30.html

Next: Recursion Up: Tools Previous: Induction Finite Differences The method of finite differences can sometimes be used to guess a formula f n ) (but not to prove it). The way I am about to describe it requires that the values of f n ) be given for integer values of n beginning with n =0 (rather than 1). Let's use the example of guessing the formula for the sum of the cubes of the first n positive integers. We calculate a few values: and then arrange them in a row. Then we build a difference table beneath them by subtraction: We continue generating rows by this process until it appears that we get a row of 0's. This does not always happen, but when it does, we can build a polynomial formula for f n ). Using the first entries in each row, multiply the first entry of the first row by 1/0!, the first entry of the second row by n /1!, the first entry of the third row by n n -1)/2!, the first entry of the fourth row by n n n -2)/3!, the first entry of the fifth row by n n n n -3)/4!, etc., and then add the results. (Remember that 0! is defined to be 1.) In our example, we get which simplifies (you try it!) to

79. FDTD.org Home log in! finiteDifference Time-Domain Literature Database the Three-Dimensional finite-Difference Time-Domain Method to Antennas Using the finite-Difference Time-Domain Method, J. http://www.fdtd.org/

home search theses journals ... feedback Certificate changed; details here Please log in! Finite-Difference Time-Domain Literature Database Citations with most recent comments: Numerical Solution of Initial Boundary Value Problems Involving Maxwell's Equations in Isotropic Media , K. S. Yee, IEEE Transactions on Antennas and Propagation , vol. 14, no. 3, 302-307, March, 1966. (bibkey=yee1966a) Comment Page (1 comment to date, last on 2003-02-09 at 07:23) Numerical Modeling of Microstrip Circuits and Antennas , D. M. Sheen, Cambridge, MA, Massachusetts Institute of Technology, 1991. (bibkey=sheen1991m) Comment Page (7 comments to date, last on 2003-03-06 at 03:08) Extending PML Absorbing Boundary Condition to Truncate Microstrip Line in Nonuniform 3-D FDTD Grid , T. Li, W. Sui, and M. Zhou, IEEE Transactions on Microwave Theory and Techniques , vol. 47, no. 9, 1771-1776, September, 1999. (bibkey=li1999a) Comment Page (24 comments to date, last on 2002-11-03 at 18:58) Far-Field Time-Domain Calculation from Aperture Radiators Using the FDTD Method , D. Sullivan and J. L. Young

80. ENVI2200 Dynamical Systems - Lecture 6 (1). is the definition of the derivative. 6.2 Recap finitedifference approximations whereDx = x j+1 -x j . 6.3 An example of a finite-difference approximation. http://www.env.leeds.ac.uk/envi2200/lecture6/lecture6.html

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