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BibTeX entry
@Article{Sheshadri:2011:MPS,
author = "K. Sheshadri and Peter Fritzson",
title = "{MathPDE}: A Package to Solve {PDEs} by Finite
Differences",
journal = j-MATHEMATICA-J,
volume = "13",
number = "??",
pages = "??--??",
month = "????",
year = "2011",
CODEN = "????",
ISSN = "1047-5974 (print), 1097-1610 (electronic)",
bibdate = "Sat Mar 15 08:18:42 MDT 2014",
bibsource = "http://www.math.utah.edu/pub/tex/bib/mathematicaj.bib",
URL = "http://www.mathematica-journal.com/2011/12/mathpde-a-package-to-solve-pdes-by-finite-differences/",
abstract = "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.",
acknowledgement = ack-nhfb,
journal-URL = "http://www.mathematica-journal.com/",
}
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