Electron. J. Diff. Eqns., Vol. 2008(2008), No. 95, pp. 1-12.

Linear matrix differential equations of higher-order and applications

Rajae Ben Taher, Mustapha Rachidi

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 5, 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.

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  Rajae Ben Taher
Département de Mathématiques et Informatique
Faculté des Sciences, Université Moulay Ismail
B.P. 4010, Beni M'hamed, Méknés, Morocco
email: bentaher@fs-umi.ac.ma
Mustapha Rachidi
Mathematics Section LEGT - F. Arago, Académie de Reims
1, Rue F. Arago, 51100 Reims, France
email: mu.rachidi@hotmail.fr

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