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Homotopy perturbation-reproducing kernel method for nonlinear systems of second order boundary value problems. (English) Zbl 1209.65078
Summary: Based on the homotopy perturbation method (HPM) and the reproducing kernel method (RKM), a new method is presented for solving systems of second order nonlinear 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. The 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.
MSC:
65L10Boundary value problems for ODE (numerical methods)
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
34B15Nonlinear boundary value problems for ODE
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