A Method of Lines Framework in Mathematica

Date of Online Publication: 31/03/2008
Keywords: MOL, Method of Lines
Authors: R. Knapp
Pages: 43-59
Mathematica’s NDSolve command includes a general solver for partial differential equations 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 ODEs or DAEs 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.

 

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