Solving Riccati differential equation using Adomian's decomposition method

Abstract

In this paper, we suggest a method to solve the matrix Riccati differential equation. The suggested method, which we called multistage Adomian's decomposition method (MADM), can be considered as an extension of the Adomian's decomposition method (ADM) which is very efficient in solving a variety of differential and algebraic equations. The solution is introduced in a recursive form which can be used to obtain the solution for the whole time horizon. Comparisons are made between MADM and the exact solution and further between MADM and different numerical methods.