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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:

65L10 | Numerical solution of boundary value problems involving ordinary differential equations |

34A25 | Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. |

34B15 | Nonlinear boundary value problems for ordinary differential equations |

### Keywords:

analytical approximation; nonlinear systems of second order boundary value problems; reproducing kernel method; homotopy perturbation method; series solution; numerical examples
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\textit{F. Geng} and \textit{M. Cui}, J. Comput. Appl. Math. 235, No. 8, 2405--2411 (2011; Zbl 1209.65078)

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### References:

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