An efficient method based on operational matrices of Bernoulli polynomials for solving matrix differential equations

Abstract

The current paper deals with elaborating a novel framework for solving a class of linear matrix differential equations. To this end, the operational matrices of integration and the product based on the shifted Bernoulli polynomials are presented and a general procedure for forming this matrices is given. The properties of this matrices are exploited to reduce the main problem to a linear matrix equation. Numerical experiments are reported to demonstrate the applicably and efficiency of the propounded technique.