A new approach for solving the first-order linear matrix differential equations

Abstract. The main contribution of the current paper is to propose a new effective numerical method for solving the firstorder linear matrix differential equations. Properties  of the Legendre basis operational matrix of integration together with a collocation method are applied to reduce the problem to a coupled linear matrix equations. Afterwards, an iterative algorithm is examined for solving the obtained coupled linear matrix equations. Numerical experiments are presented to demonstrate the applicably and efficiency of our method.