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Title

A general symbolic PDE solver generator: Beyond explicit schemes
Authors

K. Sheshadri
Organization: Linköping University
Department: Department of Computer and Information Science
Peter Fritzson
Organization: Linköping University
Department: Department of Computer and Information Science
Journal / Anthology

Scientific Programming
Year: 2003
Volume: 11
Page range: 225-235
Description

This paper presents an extension of our Mathematica- and MathCode-based symbolic-numeric framework for solving a variety of partial differential equation (PDE) problems. The main features of our earlier work, which implemented explicit finite-difference schemes, include the ability to handle (1) arbitrary number of dependent variables, (2) arbitrary dimensionality, and (3) arbitrary geometry, as well as (4) developing finite-difference schemes to any desired order of approximation. In the present paper, extensions of this framework to implicit schemes and the method of lines are discussed. While C++ code is generated, using the MathCode system for the implicit method, Modelica code is generated for the method of lines. The latter provides a preliminary PDE support for the Modelica language. Examples illustrating the various aspects of the solver generator are presented.
Subject

*Applied Mathematics > Computer Science
Keywords

symbolic-numeric framework, partial differential equation (PDE), C++