Document Type : Research Paper

Authors

• Fadhel S Fadhel ¹
• Huda Omran Altaie ²

¹ Department of Mathematics and Computer Applications, College of Science, Al-Nahrain University, Iraq.

² Department of Mathematics, College of Education For Pure Scineces, Ibn Al-Haitham, University of Baghdad, Iraq.

Abstract

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. ‎

Keywords

• Riccati matrix differential equation
• Variational iteration method
• Differential equation
• He's method
• Exact ‎solution
• Approximate solutions.‎