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Symbolic Discretization of PDEs

Rob Knapp
Organization: Wolfram Research, Inc.
Department: Kernel Technology

2004 International Mathematica Symposium
Conference location

Banff, Canada

The NDSolve command in Mathematica solves initial-boundary value partial differential equation problems using the numerical method of lines. The method of lines works by discretizing with respect to all but one of the independent variables, resulting in a system of ODEs, which is solved numerically. NDSolve is able to solve a wide variety of PDEs with a selection of discretization parameters because the discretization can be represented symbolically as a Mathematica expression, making it relatively easy to adjust parameters to fit the problem. This paper shows how the symbolic discretization can be set up and used to provide a general solver for PDEs.

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Differential Equations

symbolic discretization, PDE, NDSolve, general solver
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