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Learning about Differential Equations from Their Symmetries

Scott A. Herod
Organization: University of Colorado, Boulder
Department: Department of Applied Mathematics
Journal / Anthology

The Mathematica Journal
Year: 2004
Volume: 9
Issue: 2
Page range: 334-348

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

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.

*Mathematics > Calculus and Analysis > Differential Equations