I’ve been using Mathematica since February 1994 and I’m an expert at writing efficient and elegant Mathematica code. You might find this short handout for doing applied mathematics in Mathematica helpful.
The below packages were tested up through Mathematica version 7. They may not work correctly in version 8 or higher.
Our Painlevé test software, PainleveTest.m, performs the standard Painlevé test on systems of nonlinear polynomial ordinary and partial differential equations (ODEs and PDEs). For more information, see our paper Symbolic software for the Painlevé test of nonlinear ordinary and partial differential equations.
Package: PainleveTestV2.m
Notebook: PainleveTestV2.nb
Older Versions: PainleveTest.m;
PainleveTests.nb
Our software searches for solitary wave solutions expressible in hyperbolic and elliptic functions.
The software, PDESpecialSolutions.m, allows for the computation of solutions expressible in hyperbolic tangent, hyperbolic secant, and Jacobi ellitpic functions. For more information, see our paper Symbolic computation of exact solutions expressible in hyperbolic and elliptic functions for nonlinear PDEs.
Package: PDESpecialSolutionsV3.m
Notebook:
PDESpecialSolutionsV3--Documentation--Examples-in-Paper.nb;
PDESpecialSolutionsV3--Documentation--Additional-Examples.nb;
PDESpecialSolutionsV3--Documentation--More-Examples.nb; and
PDESpecialSolutionsV3--Documentation--Extra-Examples.nb;
Older Versions (V2):
PDESpecialSolutionsV2.m and
PDESpecialSolutions--Documentation.nb
Older Versions (V1):
PDESpecialSolutions.m;
PDESpecialSolutions--Documentation.nb;
PDESpecialSolutions--Examples.nb ; and,
PDESpecialSolutions--More--Examples.nb
The software, DDESpecialSolutions.m, allows for the computation of solutions expressible in hyperbolic tangent functions. For more information, see our paper Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations.
Package: DDESpecialSolutionsV3.m
Notebook:
DDESpecialSolutionsV3--Documentation.nb
Older Versions (V2):
DDESpecialSolutionsV2.m and
DDESpecialSolutions--Documentation.nb
Older Versions (V1):
DDESpecialSolutions.m;
DDESpecialSolutions--Documentation.nb; and,
DDESpecialSolutions--Examples.nb
The software, PDERecursionOperator.m, generates a candidate recursion operator and tests it using the defining equation (Lie derivative). For more information, see our paper Symbolic algorithms for the Painlevé test, special solutions, and recursion operators for nonlinear PDEs.
Package: RecursionOperator.m and
InvariantsSymmetries.m (by Ü. Göktas is required)
Notebook:
RecursionOperator--Documentation.nb