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Reproducing Kernel Method for Singularly Perturbed One-Dimensional Initial-Boundary Value Problems with Exponential Initial Layers

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In this paper, a meshless numerical method is proposed for singularly perturbed one-dimensional initial-boundary value problems with exponential initial layers. The method is a combination of the domain decomposition method… Click to show full abstract

In this paper, a meshless numerical method is proposed for singularly perturbed one-dimensional initial-boundary value problems with exponential initial layers. The method is a combination of the domain decomposition method and the reproducing kernel method. A fitted reproducing kernel is constructed for initial layer domain problem. Some numerical results confirming the expected behavior of the method are shown.

Keywords: singularly perturbed; reproducing kernel; initial boundary; one dimensional; perturbed one; dimensional initial

Journal Title: Qualitative Theory of Dynamical Systems
Year Published: 2018

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