Variational Iteration Method for Solving Riccati Matrix Differential Equations - Khalid Hammood Al-jiz; Noor Atinah Ahmad; Fadhel Subhi Fadhel (Institute of Advanced Engineering and Science, 2017)
Riccati matrix differential equation has long been known to be so difficult to solve analytically and/or numerically. In this connection, most of the recent studies are concerned with the derivation of the necessary conditions that ensure the existence of the solution. Therefore, in this paper, He’s Variational iteration method is used to derive the general form of the iterative approximate sequence of solutions and then proved the convergence of the obtained sequence of approximate solutions to the exact solution. This proof is based on using the mathematical induction to derive a general formula for the upper bound proved to be converge to zero under certain conditions.