A general symbolic PDE solver generator: Beyond explicit schemes
2003 (English)In: Scientific Programming, ISSN 1058-9244, E-ISSN 1875-919X, Vol. 11, no 3, 225-235 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
IOS Press, 2003. Vol. 11, no 3, 225-235 p.
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:liu:diva-109751OAI: oai:DiVA.org:liu-109751DiVA: diva2:741170