Bernoulli Matrix Approach For Matrix Differential Models Of Second-Order

In this paper, a novel effective numerical method for solving linear matrix differential equations of second order based on shifted Bernoulli polynomials is presented. Operational matrices of product and integration of shifted Bernoulli polynomials are introduced and are used to reduce the problem to a linear matrix equation. An estimation of the approximation error of presented method is provided. Finally, the applicability and efficiency of suggested technique are reported of numerical illustrative examples.