Testing regularity of functional equations with computer

Abstract

One of the standard methods of solving functional equations is reducing the equations to a form which is easily handled by the methods of analysis, for example differential equations, partial differential equations, integral equations, etc. For the reduction we must know some “strong” regularity properties of the unknown functions, which regularity follows from the “week” properties of the known functions. Our long-term plan is to create a method not only for specialists in research but for professionals in other areas using functional equations—for example engineers, economists. As a first attempt we worked out a program for some particular, but fairly general type of equations in the Computer Algebra System Maple©, which enables an easy detection of the applicability of known regularity theorems.