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Scientific Programming
Volume 11, Issue 3, Pages 225-235
http://dx.doi.org/10.1155/2003/720214

A General Symbolic PDE Solver Generator: Beyond Explicit Schemes

K. Sheshadri and Peter Fritzson

Programming Environment Laboratory, Department of Computer and Information Science, Linköping University, S-581 83 Linköping, Sweden

Received 28 July 2003; Accepted 28 July 2003

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.