solution of riccati matrix differential equation using new approach of variational ‎iteration method

To obtain the approximate solution to riccati matrix differential equations, a new variational iteration approach was ‎proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the ‎exact solution. this technique was found to give very accurate results in a few number of iterations. in this paper, the ‎modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact ‎solution of the derived sequence of approximate solutions is also stated and proved. two examples were also solved, which ‎shows the reliability and applicability of the proposed approach. ‎