MathPDE: A Package to Solve PDEs by Finite Differences
2011 (English)In: The Mathematica journal, ISSN 1047-5974, E-ISSN 1097-1610, Vol. 13Article in journal (Refereed) Published
A package for solving time-dependent partial differential equations (PDEs), MathPDE, is presented. It implements finite-difference methods. After making a sequence of symbolic transformations on the PDE and its initial and boundary conditions, MathPDE automatically generates a problem-specific set of Mathematica functions to solve the numerical problem, which is essentially a system of algebraic equations. MathPDE then internally calls MathCode, a Mathematica-to-C++ code generator, to generate a C++ program for solving the algebraic problem, and compiles it into an executable that can be run via MathLink. When the algebraic system is nonlinear, the Newton-Raphson method is used and SuperLU, a library for sparse systems, is used for matrix operations. This article discusses the wide range of PDEs that can be handled by MathPDE, the accuracy of the finite-difference schemes used, and importantly, the ability to handle both regular and irregular spatial domains. Since a standalone C++ program is generated to compute the numerical solution, the package offers portability.
Place, publisher, year, edition, pages
Wolfram Research , 2011. Vol. 13
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:liu:diva-109733OAI: oai:DiVA.org:liu-109733DiVA: diva2:741079