Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 95, pp. 1-12.
Title: Linear matrix differential equations of higher-order and
applications
Authors: Rajae Ben Taher (Univ. Moulay Ismail, Meknes, Morocco)
Mustapha Rachidi (Academie de Reims, Morocco)
Abstract:
In this article, we study linear differential equations
of higher-order whose coefficients are square matrices.
The combinatorial method for computing the matrix powers
and exponential is adopted. New formulas representing
auxiliary results are obtained. This allows us to prove
properties of a large class of linear matrix differential
equations of higher-order, in particular results of Apostol and
Kolodner are recovered. Also illustrative examples and
applications are presented.
Submitted February 25, 2007 Published July 05, 2008.
Math Subject Classifications: 15A99, 40A05, 40A25, 15A18.
Key Words: Algebra of square matrices; linear recursive relations;
matrix powers; matrix exponential;
linear matrix differential equations.