Transforming Systems of PDEs for Efficient Numerical Solution
1999 (English)Conference paper (Refereed)
A Mathematica package to deal with a system of partial differential equations (PDEs) is presented. This package usesexplicit finite−difference schemes to handle equations in an arbitrary number of variables that are functions of onespatial variable and time. The code has the flexibility to incorporate any difference approximation specified by theuser, 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. Examples are presented in which the generated C++ code runs about a thousand times faster than the Mathematica code.
Place, publisher, year, edition, pages
PDE, partial differential equation, finite-difference, difference approximation, discrete initial conditions, discrete boundary conditions, MathCode C++
Electrical Engineering, Electronic Engineering, Information Engineering
IdentifiersURN: urn:nbn:se:liu:diva-110165OAI: oai:DiVA.org:liu-110165DiVA: diva2:743226
Third International Mathematica Symposium (IMS 1999), Linz, Austria