Andreas Wrangsjö, Peter Fritzson and K. Sheshadri

Department of Computer and Information Science

Linköping University, S-581 83 Linköping, Sweden

Email: {andwr, petfr, shesh}@ida.liu.se

Phone: +46 13 281484, Fax: +46 13 284499

**Abstract**

A Mathematica package to deal with a system of partial differential
equations (PDEs) is presented. This package uses explicit finite-difference
schemes to handle equations in an arbitrary number of variables that are
functions of one spatial variable and time. The code has the flexibility
to incorporate any difference approximation specified by the user, and
transforms the given system of PDEs into a system of difference equations
that can be iteratively solved using the discretized forms of initial and
boundary conditions. The iteration is made considerably faster by converting
the Mathematica code into an optimized C++ code using the MathCode C++
compiler[1]. Examples are presented in which the generated C++ code runs
about a thousand times faster than the Mathematica code.