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MathGroup Archive 2004

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Re: Mathematica software for pde

  • To: mathgroup at smc.vnet.net
  • Subject: [mg45643] Re: [mg45611] Mathematica software for pde
  • From: CAP F <Ferdinand.Cap at eunet.at>
  • Date: Fri, 16 Jan 2004 19:57:58 -0500 (EST)
  • References: <200401161105.GAA10718@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Mark Coleman wrote:
> 
> Hi,
> 
> I'm searching for Mathematica code to solve 2 or 3-dimensional nonconstant
> coefficient convection-diffusion pde's, with free boundary conditions
> (these pde's are often used to model problems in quantitative finance
> involving certain types of options securities). I have seen various
> references to pde solvers written in Mathematica, but I have not done an
> exhaustive search. I was hoping someone on MathGroup might be able to
> point me in the right direction. Alternatively, if there are
> established C or FORTRAN code libraries that I could compile and link
> via MathLink, that would be very helpful as well.
> 
> Thanks.
> 
> Regards,
> 
> Mark

Mathematical Methods of Physics and Engineering with Mathematica
Ferdinand F . Cap, CRC-Press/Chapman and Hall, 2003,
ISBN 1584884029,  56 Codes  to be downloaded from 
www.crcpress.com

1 Introduction
1.1 What is a boundary problem?
1.2 Classification of partial differential equations
1.3 Types of boundary conditions and the collocation method
1.4 Differential equations as models for nature

2 Boundary problems of ordinary differential equations
2.1 Linear differential equations
2.2 Solving linear differential equations
2.3 Differential equations of physics and engineering
2.4 Boundary value problems and eigenvalues
2.5 Boundary value problem as initial value problem
2.6 Nonlinear ordinary differential equations
2.7 Solutions of nonlinear differential equations

3 Partial differential equations
3.1 Coordinate systems and separability 
3.2 Other methods to reduce partial to ordinary differential 
equations
3.3 The method of characteristics
3.4 Nonlinear partial differential equations

4 Boundary problems with one closed boundary defined by 
coordinate lines

4.1 Laplace and Poisson equation
4.2 Conformal mapping in two and three dimensions
4.3 D'Alembert wave equation and string vibrations
4.4 Helmholtz equation and membrane vibrations
4.5 Rods and the plate equation
4.6 Approximation methods
4.7 Variational calculus
4.8 Collocation methods

5 Boundary problems with two closed boundaries
5.1 Inseparable problems
5.2 Holes in the domain.Two boundaries belonging to different
coordinate systems
5.3 Corners in the boundary

6 Nonlinear boundary problems
6.1 Some definitions and examples
6.2 Moving and free boundaries
6.3 Waves of large amplitudes. Solitons
6.4 Rupture of an embankment-type dam
6.5 Gas flow in a combustion engine

List of codes (1 - 56)
see:  www.crcpress.com/downloads
(F.Cap,  Mathematical Methods in Physics and Engineering with
Mathematica, ccrcpress and Chapman and Hall,  2003, ISBN 
1584884029


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