Homotopy perturbation-reproducing kernel method for nonlinear systems of second order boundary value problems

Authors:
Fazhan Geng;Minggen Cui
Affiliations:
Department of Mathematics, Changshu Institute of Technology, Changshu, Jiangsu 215500, China;Department of Mathematics, Harbin Institute of Technology, Weihai, Shandong 264209, China
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

In this paper, based on homotopy perturbation method (HPM) and reproducing kernel method (RKM), a new method is presented for solving nonlinear systems of second order boundary value problems (BVPs). HPM is based on the use of traditional perturbation method and homotopy technique. The HPM can reduce a nonlinear problem to a sequence of linear problems and generate a rapid convergent series solution in most cases. RKM is also an analytical technique, which can solve powerfully linear BVPs. Homotopy perturbation-reproducing kernel method (HP-RKM) combines advantages of these two methods and therefore can be used to solve efficiently systems of nonlinear BVPs. Three numerical examples are presented to illustrate the strength of the method.