The Mathematica Journal
Volume 9, Issue 2

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Learning about Differential Equations from Their Symmetries
Scott A. Herod

Symmetries form the basis of the packages DSolve and PDSolve1. A knowledge of symmetries facilitates the understanding and analysis of solutions of differential equations and an understanding of the techniques used to solve the equations. This article introduces a package, MathSym, that assists in the computation of symmetries. MathSym's flexibility and utility are illustrated through four examples, two from ordinary differential equations and two from partial differential equations.

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  *Introduction

  *Reductions of Differential Equations: Scaling Symmetries

  *Application of MathSym to Analyzing an Ordinary Differential Equation

  *Application of MathSym to Analyzing a Partial Differential Equation

  *Closing Comments

  *Input Files

  *Acknowledgments

  *References

  *Additional Material

 
About the Author
Scott A. Herod did postdoctoral research at the University of Colorado in Boulder where his interests included differential equations, dynamical systems, and computational mathematics. He now works as a software consultant specializing in the video industry.

Scott A. Herod
Department of Applied Mathematics
University of Colorado, Boulder
Campus Box 526
Boulder, Colorado 80309-0526
scott.herod@colorado.edu


     
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