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In Wang et al., 2011 , we give an iterative reproducing kernel method IRKM . The main contribution of this paper is to use an IRKM Wang et al., 2011 , in singular perturbation problems with boundary layers. Two numerical examples are studied to demonstrate the accuracy of the present method. Results obtained by the method indicate that the method is simple and effective.

We use the reproducing kernel method to solve the well-known classes of Lane-Emden-type equations. These classes of equations have the form of Lane-Emden problem. Comparing the results of the reproducing kernel method with the analytical solutions by means of some typical examples, we can affirm that the reproducing kernel method is an efficient and accurate method.

We give the analytical solution and the series expansion solution of a class of singularly perturbed partial differential equation (SPPDE) by combining traditional perturbation method (PM) and reproducing kernel method (RKM). The numerical example is studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective.

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