Reproducing kernel method for singularly perturbed one-dimensional initial-boundary value problems with exponential initial layers. (English) Zbl 1448.65079
Summary: 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.
MSC:
| 65L11 | Numerical solution of singularly perturbed problems involving ordinary differential equations |
| 65L03 | Numerical methods for functional-differential equations |
Keywords:
reproducing kernel methods; exponential initial layers; initial-boundary value problems; singularly perturbed problemsReferences:
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