A piecewise variational iteration method for Riccati differential equations

Authors:
Fazhan Geng;Yingzhen Lin;Minggen Cui
Affiliations:
Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China and Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China;Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China;Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

In this paper, we introduce a piecewise variational iteration method for Riccati differential equations, which is a modified variational iteration method (MVIM). The solutions of Riccati differential equations obtained using the traditional variational iteration method (VIM) give good approximations only in the neighborhood of the initial position. However, the solutions obtained using the MVIM give good approximations for a larger interval, rather than a local vicinity of the initial position. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method. Numerical results show that the method does not share the drawback of the conventional VIM and is a satisfactory method for Riccati differential equations.