Aequationes mathematicae

, Volume 67, Issue 1–2, pp 47–62 | Cite as

Solving linear two variable functional equations with computer

  • Attila HázyEmail author
Research paper


In the present paper we deal with the linear two variable functional equation \( h_{0}(x,y)f_{0}(g_{0}(x,y)) + \cdots + h_{n}(x,y)f_{n}(g_{n}(x,y)) = F(x,y) \) where n is a positive integer, \( g_{0}, g_{1}, \ldots, g_{n}, h_{0}, h_{1}, \ldots, h_{n}, \) and F are given real valued analytic functions on an open set \( \Omega \subset \mathbb{R}^2, \) furthermore \( f_{0}, f_{1}, \ldots, f_{n} \) are unknown functions.

Applying the results of Páles [3] we get recursively an inhomogeneous linear differential-functional equation in one of unknown function for f0, then for \( f_{1}, f_{2}, \ldots, f_{n}, \) 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 differential-functional equation.

Our aim is also to describe a computer-program which solves functional equations of this type.

The theoretical background of the program is based on the result and algorithm of Páles [3] and our main results. This algorithm is implemented in Maple VR4 symbolic language.

Mathematics Subject Classification (2000).



Functional equation. 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of MiskolcMiskolc-EgyetemvárosHungary

Personalised recommendations