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International Journal of Mathematics and Mathematical Sciences
Volume 17, Issue 1, Pages 91-102
http://dx.doi.org/10.1155/S016117129400013X

Solving higher order Fuchs type differential systems avoiding the increase of the problem dimension

Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, P.O. Box 22.012, Valencia, Spain

Received 26 June 1992

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, we develop a Frobenius matrix method for solving higher order systems of differential equations of the Fuchs type. Generalized power series solution of the problem are constructed without increasing the problem dimension. Solving appropriate algebraic matrix equations a closed form expression for the matrix coefficient of the series are found. By means of the concept of a k-fundamental set of solutions of the homogeneous problem an explicit solution of initial value problems are given.