An ε-Uniform Hybrid Scheme for Singularly Perturbed 1-D Reaction-Diffusion Problems

S. Natesan (), R.K. Bawa () and C. Clavero ()
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S. Natesan: Indian Institute of Technology, Department of Mathematics
R.K. Bawa: Punjabi University, Department of Computer Science and Engineering
C. Clavero: Universidad de Zaragoza, Departamento de Matemática Aplicada

A chapter in Numerical Mathematics and Advanced Applications, 2006, pp 1079-1087 from Springer

Abstract: Abstract An ε-uniform second-order numerical method for singularly perturbed reaction-diffusion problems is proposed in this article. The difference scheme is based on cubic spline and classical finite difference scheme, which is applied on layer resolving Shishkin meshes. Uniform stability and uniform convergence of the scheme in the maximum norm are studied. A numerical example is presented to support the theoretical results.

Date: 2006
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DOI: 10.1007/978-3-540-34288-5_108

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