Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2012, Special Issue (2012), Article ID 603748, 8 pages.
A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods
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.
Abstr. Appl. Anal., Volume 2012, Special Issue (2012), Article ID 603748, 8 pages.
First available in Project Euclid: 1 April 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Geng, F. Z.; Li, X. M. A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods. Abstr. Appl. Anal. 2012, Special Issue (2012), Article ID 603748, 8 pages. doi:10.1155/2012/603748. https://projecteuclid.org/euclid.aaa/1364845168