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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

Summary.

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).

39B22. 

Keywords.

Functional equation. 

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Copyright information

© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of MiskolcMiskolc-EgyetemvárosHungary

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