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Zbl 1189.65164
Geng, Fazhan; Lin, Yingzhen; Cui, Minggen
A piecewise variational iteration method for Riccati differential equations. (English)
[J] Comput. Math. Appl. 58, No. 11-12, 2518-2522 (2009). ISSN 0898-1221

Summary: 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.

MSC 2000:: *65L99 Numerical methods for ODE
34A45 Theoretical approximation of solutions of ODE

Keywords: piecewise variational iteration method; modified variational iteration method; Riccati differential equation

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