A general symbolic PDE solver generator: Beyond explicit schemes

Article type: Research Article

Authors: Sheshadri, K. | Fritzson, Peter

Affiliations: Programming Environment Laboratory, Department of Computer and Information Science, Linköping University, S-581 83 Linköping, Sweden. E-mail: {shesh,petfr}@ida.liu.se

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.

Journal: Scientific Programming, vol. 11, no. 3, pp. 225-235, 2003