Open Access
2012 A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods
F. Z. Geng, X. M. Li
Abstr. Appl. Anal. 2012(SI12): 1-8 (2012). DOI: 10.1155/2012/603748

Abstract

We introduce a new method for solving Riccati differential equations, which is based on reproducing kernel method and quasilinearization technique. The quasilinearization technique is used to reduce the Riccati differential equation to a sequence of linear problems. The resulting sets of differential equations are treated by using reproducing kernel method. The solutions of Riccati differential equations obtained using many existing methods give good approximations only in the neighborhood of the initial position. However, the solutions obtained using the present method give good approximations in a larger interval, rather than a local vicinity of the initial position. Numerical results compared with other methods show that the method is simple and effective.

Citation

Download Citation

F. Z. Geng. X. M. Li. "A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods." Abstr. Appl. Anal. 2012 (SI12) 1 - 8, 2012. https://doi.org/10.1155/2012/603748

Information

Published: 2012
First available in Project Euclid: 1 April 2013

zbMATH: 1237.65090
MathSciNet: MR2898051
Digital Object Identifier: 10.1155/2012/603748

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI12 • 2012
Back to Top