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Solving a class of singularly perturbed partial differential equation by using the perturbation method and reproducing kernel method. (English) Zbl 1474.65339

Summary: 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.

MSC:

65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
35L50 Initial-boundary value problems for first-order hyperbolic systems
35B25 Singular perturbations in context of PDEs
35L65 Hyperbolic conservation laws
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