A new method for determining the solution of Riccati differential equations

摘要

This paper presents a new and efficient approach for determining the solution of Riccati differential equation. The Riccati equation is first converted to a second-order linear ordinary differential equation, and then to a Volterra integral equation. By solving the resulting Volterra equation by means of Taylor’s expansion, the approximate solution of Riccati differential equation is obtained, which can be achieved by symbolic computation. The accuracy of approximate solution can be further improved with the increase of the order of approximations. An error analysis is given. Test examples demonstrate the effectiveness of the method. A comparison between the present results with previous results is made, inferring that the suggested method is not only enough accurate but also quite stable.