The Application of Asymptotic Analysis for Developing Reliable Numerical Method for a Model Singular Perturbation Problem

Date of Online Publication: 27/10/2007
Keywords: Singular perturbation problem; asymptotic analysis; finite difference methods
Authors: Kailash C. Patidar and Albert Shikongo
Pages: 193-207
This paper deals with the design and implementation of some appropriate numerical methods for a model singularly perturbed differential equation. To adapt the local abrupt changes of the solution, we consider a piecewise uniform mesh instead of uniform mesh throughout the underlying interval. For designing appropriate grid, some apriori information about the width of boundary layer (denoted by ?) is always helpful. We use asymptotic analysis to find out this information about ?. Based on this information on ?, we design a fitted mesh numerical method. Numerical results for this method and those corresponding to its standard analogue are presented.


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