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

‎The main contribution of the current paper is to propose a new effective numerical method for solving the first-order 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.