Solving functional equations with computer

Házy, Attila (2013) Solving functional equations with computer. In: IEEE 4th International Conference on Cognitive Infocommunications, CogInfoCom 2013, December 2-5, 2013., 2013.12.02-2013.12.05., Budapest.

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Abstract

In this paper we deal with the linear two variable functional equation ℎ_0(x,y)f_0(g_0(x,y))+⋅⋅⋅+ℎ_n(x,y)f_n(g_n(x,y))=F(x,y) where n is a positive integer, g_0, g_1,..., g_n, h_0,ℎ_1,...,ℎ_n and F are given real valued analytic functions on an open set Ω ⊂ ℝ^2,furthermore f_0,f_1,...,f_n are unknown functions. Applying the results of Páles we get recursively an inhomogeneous linear differential-functional equation in one of unknown function for f_1,f_2,...,f_n, respectively. One of our main result states that the solutions of the differential-functional equation obtained are the same as that of an ordinary differential equation (under some assumptions), whose order is usually much smaller than the order of the differetial-functional equation. Our aim is also to describe a computer-program which solves functional equations of this type. This algorithm is implemented in Maple symbolic language.

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