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Iterative reproducing kernel method for solving second-order integrodifferential equations of Fredholm type. (English) Zbl 1442.65458

Summary: We present an efficient iterative method for solving a class of nonlinear second-order Fredholm integrodifferential equations associated with different boundary conditions. A simple algorithm is given to obtain the approximate solutions for this type of equations based on the reproducing kernel space method. The solution obtained by the method takes form of a convergent series with easily computable components. Furthermore, the error of the approximate solution is monotone decreasing with the increasing of nodal points. The reliability and efficiency of the proposed algorithm are demonstrated by some numerical experiments.

MSC:

65R20 Numerical methods for integral equations
45B05 Fredholm integral equations
45J05 Integro-ordinary differential equations
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