The Mathematica Journal
Volume 9, Issue 2


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Learning about Differential Equations from Their Symmetries
Scott A. Herod

Input Files

MathSym uses input files for the information that it needs. I decided to do this because the amount of information that the package needs is reasonably large, and I have found it useful to keep a record of all of the necessary information needed to run a particular problem.

The first two input files do not include the three optional arguments that occur in the input file for the nonlinear Schrödinger equation. The defaults for these variables are discussed in the documentation, which is part of the standard distribution of MathSym. The first listing is for the example of the heat equation discussed in the first section, Reductions of Differential Equations: Scaling Symmetries. It is also included in Additional Material in the file named Heat_eqn.m. The second listing contains the information for the ordinary differential equation described in Application of MathSym to Analyzing an Ordinary Differential Equation, and is contained in the file ODE_eqn.m. Finally, the input file for the nonlinear Schrödinger equation from the section Application of MathSym to Analyzing a Partial Differential Equation is listed in the third input cell. This information is also contained in the file NLS_eqn.m in Additional Material.

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