Document Type : Research Paper
Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Iraq.
Department of Mathematics, College of Education For Pure Scineces, Ibn Al-Haitham, University of Baghdad, Iraq.
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.