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Solving Functional Equations With a Computer Algebra System: Examples and Applications

Andrés Iglesias
Organization: University of Cantabria
Department: Department of Applied Mathematics and Computational Science
Akemi Gálvez
Organization: University of Cantabria, Santander, Spain

2002 Applications of Computer Algebra Conference (ACA '2002)
Conference location

Volos, Greece

This talk introduces the symbolic treatment of functional equations and presents a Mathematica package for the solution of functional equations of one and several variables. The package allows the user to solve an interesting set of functional equations with its four components: equation, domain, class and the corresponding solution. The package incorporates a searching algorithm which can solve functional equations independently of its notation and its algebraic representation. Not only general solutions but particular and candidate solutions are dealt with. This implies a careful analysis of domains and classes. The package includes some methods for solving functional equations. Some examples illustrate the use of the package. Finally, interesting applications to several fields are also discussed.

*Mathematics > Algebra

functional equations, equation, domain, class, corresponding solution, computer algebra system