Geometry.Net - Math_Help_Desk: Equation Solvers

Sandia National Laboratories - LDRD Enhancing Multilevel Linear Equation Solvers
Enhancing Multilevel Linear equation solvers Using Domain Decomposition StrategiesPrincipal Investigator John RedHorse. Project Manager David Martinez.
http://www.sandia.gov/LDRD/EnhMulLi.htm
FEA, System Equation Solvers
FEM Solvers Evaluating System Equations. This Pageis Under Construction and will be Available Soon.
http://www.dermotmonaghan.com/fea/htm/fea_mathematics/equation_solvers.htm
Www.ma.man.ac.uk/NAC98/numerica.nb
front end, or user interface. },Text , TextJustification 1, Cell \ \ Numericslinear algebra, nonlinear equation solvers, optimization, \ differential
http://www.ma.man.ac.uk/NAC98/numerica.nb

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Center For Computational Math Colloquium, Fall 2001
Title Fast Heatequation solvers. Abstract I give fast solvers for the heatequation based on formulas of Feynman-Kac type for the pointwise solution.
http://www-math.cudenver.edu/ccm/colloq/0102/feb04.html

Extractions: CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM UNIVERSITY OF COLORADO AT DENVER PLACE: Mathematics Conference Room 626 UCD Building, 1250 14th St. , Denver TIME: NOON (Refreshments served at 11:45 am) Date: Monday, February 4, 2002 Speaker: Ben Fox Affiliation: SIM-OPT Consulting, Boulder, CO. e-mail: bfox@carbon.cudenver.edu Title: Fast Heat-Equation Solvers Abstract:
Description Of Computer Code
ü Direct symmetric and nonsymmetric matrix column equation solvers(in-core and out of-core Crout profile solvers). Symmetric
http://www.princeton.edu/~dynaflow/description_df.htm

Extractions: URL: http://www.princeton.edu/~prevost D YNAFLOW is a finite element analysis program for the static and transient response of linear and nonlinear two- and three-dimensional systems. In particular, it offers transient analysis capabilities for both parabolic and hyperbolic initial value problems in solid, structural and fluid mechanics. There are no restrictions on the number of elements, the number of load cases, the number of load-time functions, and the number or bandwidth of the equations. Despite large system capacity, no loss of efficiency is encountered in solving small problems. In both static and transient analyses, an implicit-explicit predictor-(multi)corrector scheme is used. The nonlinear implicit solution algorithms available include: successive substitutions, Newton-Raphson, modified Newton and quasi-Newton (BFGS and Broyden updates) iterations, with selective line search options. Some features which are available in the program include: Multi-field/physics analysis capabilities via selective specification of multiple solution staggers.
Numerical Objects Online
Heat equation solvers as a minor extension of the Poisson equation solvers, classTimePrm for time data, visualization of timedependent data. Ch. 3.9-3.10.
http://www.nobjects.com/resources/training_courses.html

Extractions: A good opportunity to get up to speed with your Diffpack development is to attend one of our scheduled training courses in Oslo , Norway, or local arrangements in your region. All courses will be lectured in English. The course extends over a total of 4 days and is split in two main parts: Depending on your background you might want to skip Part I. It is possible to prepare yourself for Part II by reading Chapter 1 of the course book. The course is suitable for beginners as well as more experienced Diffpack programmers. It should be ideal if you are in the process of evaluating Diffpack. Confer the course program to see what you will learn. The course may also be given as on-site training for our customers. Please contact us at course@nobjects.com
FEFLOW - Finite Element Groundwater Flow Modeling And Remediation Software
These include Fast iterative equation solvers appropriate for large systems, suchas the PCG, BiCGSTAB, CGS, Restarted GMRES, and Restarted ORTHOMIN methods
http://www.bossintl.com/html/feflow_details.html

Extractions: FEFLOW is a finite element based model with a wide selection of numerical solvers for performing complex 2D and 3D steady-state or transient groundwater flow and contaminant transport modeling. US UK UK Home ... View Cart FEFLOW Overview Features Pricing Resources Downloads Literature Services Support Consulting Home Products ... FEFLOW FEFLOW Features FEFLOW (Finite Element Flow) is one of the most sophisticated groundwater modeling packages available. The program provides an advanced 2d and 3D graphically based modeling environment for performing complex groundwater flow, contaminant transport, and heat transport modeling. Page 1 of 3 Free CD-ROM Request a free CD-ROM containing the complete FEFLOW software, along with tutorials and user documentation. Click for details Free Download Download a free, working copy of FEFLOW, analysis models, tutorials, documentation, and support utilities. Click for details Unparalleled Modeling Capability FEFLOW is a finite element based model with a wide selection of numerical solvers for performing complex 2D and 3D steady-state or transient groundwater flow and contaminant transport modeling. FEFLOWs finite element approach allows the user to quickly build a model to accurately analyze groundwater flow and transport for complex 3D geology. FEFLOW simulation capabilities include: Particle tracking and flow pathlines.
Timberlake Middle
MathematicaEnhanced Symbolic Differential equation solvers The symbolicdifferential equation solvers in Mathematica 4.1 are completely
http://www.timberlake.co.uk/software/mathematica/whatisnew_diffEqSol.html

Extractions: The symbolic differential equation solvers in Mathematica 4.1 are completely redesigned and now cover almost all classical methods. These include a new implementation of Kovacic's algorithm for solving second-order linear homogeneous differential equations with rational function coefficients, powerful new methods and symmetry techniques for solving first-order nonlinear differential equations, improved recognition of differential equations for special functions, and powerful integrating factor methods for second-order nonlinear ordinary differential equations. In addition, the methods for finding solutions of partial differential equations are upgraded significantly. The improvements in DSolve are profound and cover nearly every class of differential equations handled by Mathematica. In addition to the new and revised methods, the new code has an enhanced parser, is much more modular, and is easier to maintain. The following examples cover just a fraction of the improvements, but they should give you an overview of the breadth of enhancements in this release.
Math.com Online Solvers
You can usually find the exact answer or, if necessary, a numerical answer to almostany accuracy you require. (equation Solving Help), Help with Online solvers,
http://www.math.com/students/solvers/online_solvers.htm
High-Performance Algorithms For Analysis And Design
feedback and an Internet Challenge (comparing GPS with other solvers for NASA to calculatethe first 100 vibration modes for the 5,156 equation Next Generation
http://solvers.larc.nasa.gov/

Extractions: High-Performance Algorithms for Analysis and Design NASA's General-Purpose Solver (GPS) is a rapid matrix equation solver for large-scale structural , electromagnetic and acoustic analyses (8.3 million complex equations). GPS minimizes solution time and memory by exploiting matrix properties (sparse/dense, real/complex, symmetric), computers (sequential/parallel, from Supercomputers/Unix to PCs/Windows or Linux) and languages (FORTRAN, C++, and Java Internet Challenge (comparing GPS with other solvers for NASA benchmarks) are solicited by NASA. EIGr , a fast NASA eigensolver, calculates vibration modes and frequencies. EIGr reduced the time to calculate the first 100 vibration modes for the 5,156 equation Next Generation Space Telescope (NGST) model from 45.6 minutes to 31 seconds (88X speedup) opening the door for trade studies on more refined and accurate NGST models. To test GPS and/or EIGr, complete this form Thomas Noll, Acting Branch Head Dr.Storaasli
Quadratic Equation Tutorials, Homework Help And Problem Solvers.
Quadratic equation Tutorials solvers Guide picks. Quadratic equationtutorials, homework help and problem solvers. Complete the
http://math.about.com/cs/quadraticequation/
Math.com Online Calculators
Polynomials, functions, graphing, derivatives, limits, integration and more.Also a separate differential equation toolkit. (Vanderbilt University).
http://www.math.com/students/calculators/calculators.html

Extractions: Basic Calculator - quick and simple Scientific Calculator - full featured: logs, trig, hex Square Root - find square root of any number Circle - find area, radius, perimeter Prime Number - is it prime? Quadratic Equations - input a, b, c and find roots Percents - 3 ways to calculate percentages, percent of, etc. Alert! If your teacher doesn't allow calculators for homework, that means online ones, too.
What's New In Mathematica 4.1: Symbolic Differential Equation Solvers
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http://www.wolfram.com/products/mathematica/newin41/computing.ja.html

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Grade 7 Linear Equations 2
Grade 7 The Learning equation Math. 22.03 Linear equations singlevariable, first-degree linear equation, using concrete materials or Change the equation to show to each of the
http://cap.epsb.ca/math14_Jim/math7/strand2/2203.htm
Quadratic Equation Calculator
quadratic equation calculator, algebra, algebraic equation calculator Quadratic equation Calculator. Input MUST have the format AX2 + BX + C = 0. EXAMPLE If you have the equation 2X2
http://www.1728.com/quadratc.htm
Symplectic Integrators Versus Ordinary-differential-equation Solvers For Hamilto
Morton Hall. CD.03 Symplectic integrators versus ordinarydifferential-equationsolvers for Hamiltonian systems. Jon Lee (Wright
http://flux.aps.org/meetings/YR9596/BAPSOFM96/abs/S160003.html

Extractions: Room 219, Morton Hall Jon Lee (Wright Lab (FIB), Wright-Patterson AFB, OH 56433) In this talk, we compare the performance of symplectic integrators and ordinary-differential-equation (ODE) solvers for some low dimensional Hamiltonian systems. Considered here are the symplectic integrators of second-order (Feng, Ruth, Friedman amp; Auerbach), fourth-order (Forest amp; Ruth, Candy amp; Rozmus) and sixth-order (Yoshida), and the ODE solvers of DEABM and DERKF (Shampine) of the SLATEK library and LSODE (Hindmarsh) of ODEPACK. These integrators and solvers are used for trajectory computation of the Holmes oscillator, two-body central force field motion, and Henon-Heiles system. The main observation is that ODE solvers outperform the symplectic integrators in accuracy, but fall short in efficiency. Part C of program listing
Numerical Solvers
next Next The Mathematical Problem. Numerical Differential EquationSolvers. Robert Piché Tampere University of Technology. After
http://icosym-nt.cvut.cz/odl/partners/tut/unit2/

Extractions: Next: The Mathematical Problem Numerical Differential Equation Solvers Tampere University of Technology After you've formed a model of a physical system, you'll want to compute the solution. Usually, the model is so large and complex that you'll want to use numerical solvers rather than attempt an ``exact'' solution. You can use the numerical solvers available in your simulation software or use algorithms available in general-purpose mathematical software packages. In either case, you will be faced with a range of choices: which method to use and what solution parameters to give it. This lesson provides some guidance to help you make the right choices. A model of the dynamics of a physical system can have many different kinds of mathematical object, including ordinary differential equations, partial differential equations, algebraic equations, and difference equations (``discrete-time'' models). In this lesson, attention is restricted to models that are ordinary differential equation initial value problems. We start by giving a precise description of this mathematical problem. We then look at the general ideas behind numerical solution algorithms. We explain the difference between algorithms that are constant or variable time step, one-step or multistep, explicit or implicit, low-order or high-order.
Grade 7 Linear Equations 2
source SliderGraphApplet. OneStep Linear equation. Modified source TeachingInformal Algebra. One-step Linear equation Generator. ax = b x/a = b a/x = b.
http://dev1.epsb.edmonton.ab.ca/math14_Jim/math7/strand2/2203.htm
Magnetic Field Visualization
A new technique is described for ultra fast magnetic modelling and visualization of magnetic fields.
http://redirect-west.inktomi.com/click?u=http://www.vizimag.homestead.com/&y=028
Automatic Generation And Differentiation Of Partial Differential Equation Solver
Automatic Generation and Differentiation of Partial Differential EquationSolvers with IndexFree Scripts. Jitse Niesen. Automatic
http://www.damtp.cam.ac.uk/user/na/people/Jitse/abstract_cs.html

Extractions: Master's thesis, Department of Computer Science, University of Twente, the Netherlands, 1999. In this thesis, a system for the automatic generation of a numerical solver for partial differential equations using finite differences is developed. Due to the high performance demands in scientific computing, the efficiency of the generated code should be comparable to hand-written code. The input consists of a high-level specification of the difference scheme. Only explicit schemes are considered. Besides generating the code for the solver, the system can also automatically differentiate the difference scheme for eg.~optimisation. This automatic differentiation should take place at the script level instead of at the source-code level to retain of the general view. The input, specifying the difference scheme, is contained in a script, which is basically a sequence of assignments. However, automatic differentiation of assignments with indexed expressions leads to the difficult problem of symbolically contracting tensors containing Kronecker deltas with non-trivial index expressions. To circumvent this problem, the script are required to be index-free. Stencil operators are provided to enable the expression of difference schemes in index-free scripts. The notion of repeating a certain action is enclosed in a special stencil operator called the iterator.

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