Scientific Programming

Scientific Programming / 2003 / Article

Open Access

Volume 11 |Article ID 720214 | https://doi.org/10.1155/2003/720214

K. Sheshadri, Peter Fritzson, "A General Symbolic PDE Solver Generator: Beyond Explicit Schemes", Scientific Programming, vol. 11, Article ID 720214, 11 pages, 2003. https://doi.org/10.1155/2003/720214

A General Symbolic PDE Solver Generator: Beyond Explicit Schemes

Received28 Jul 2003
Accepted28 Jul 2003

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.

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.


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