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Solving two-point boundary value problems using combined homotopy perturbation method and Green’s function method. (English) Zbl 1166.65362
Summary: An algorithm is proposed for the solution of second-order boundary value problems with two-point boundary conditions. The Green’s function method is applied first to transform the ordinary differential equation into an equivalent integral one, which has already satisfied the boundary conditions. And then, the homotopy perturbation method is used to the resulting equation to construct the numerical solution for such problems. Numerical examples demonstrate the efficiency and reliability of the algorithm developed, it is quite accurate and readily implemented for both linear and nonlinear differential equations with homogeneous and nonhomogeneous boundary conditions. Furthermore, the lower order approximation is of higher accuracy for most cases. Some other extended applications of this algorithm are also exhibited.

MSC:
65L10Boundary value problems for ODE (numerical methods)
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
34B05Linear boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
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References:
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