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A method of lines framework in Mathematica. (English) Zbl 1154.65070
Summary: Mathematica’s NDSolve command includes a general solver for partial differential equations (PDEs) based on the method of lines. Starting from a symbolic expression for the PDE a symbolic general representation of the spatial discretization is constructed which is finalized once the differencing scheme and spatial discretization is determined. The resulting system of ordinary differential equations or differential-algebraic equations is integrated using one of the several methods available in the NDSolve framework. This paper will address how the symbolic representation of the system combines with the rest of the Mathematica system to allow exibility in discretization schemes while ultimately providing efficient evaluation and integration.

65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
68W30 Symbolic computation and algebraic computation
35-04 Software, source code, etc. for problems pertaining to partial differential equations
35L70 Second-order nonlinear hyperbolic equations
35Q53 KdV equations (Korteweg-de Vries equations)
Mathematica; NDSolve