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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 603748, 8 pages
http://dx.doi.org/10.1155/2012/603748
Research Article

A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods

Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China

Received 1 December 2011; Accepted 17 December 2011

Academic Editor: Shaher Momani

Copyright © 2012 F. Z. Geng and X. M. Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.