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

Geng, Fazhan ^[1] ; Tang, Zhiqiang ^[1] ; Zhou, Yongfang ^[2]
1. [1] Changshu Institute of Technology
  
  Changshu Institute of Technology
  
  China
2. [2] Hebei University
  
  Hebei University
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 1, 2018, págs. 177-187
Idioma: inglés
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Resumen
- 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.