An improved method for determining the solution of Riccati equations

摘要

In this paper, we present an improved method for solving Riccati equations, which possesses a fast convergence rate and high accuracy. This modification is based on a previous approach used for solving Riccati equations (Tang and Li in Appl Math Comput 194:431-440, 2007). The Riccati equation is first transformed to a second-order linear ordinary differential equation, and then to a Volterra integro-differential equation. The Taylor expansion for the unknown function and integration method are employed to reduce the resulting integral equations to a system of linear equations for the unknown and its derivatives. Also, we improve the accuracy of the obtained approximate solutions through the application of the Pade approximant. Some numerical illustrations are given to show the effectiveness of the proposed modification.