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FITTED VAN VELDHUIZEN FINITE DIFFERENCE METHOD FOR SINGULAR PERTURBATION PROBLEMS WITH LAYER BEHAVIOUR

K. Phaneendra, Y.N. Reddy and Hari Shankar Prasad

Department of Mathematics, National Institute of  Technology, Warangal-506004, INDIA. Email: kollojuphaneendra@yahoo.co.in

 

Abstract

     In this paper, we present a fitted Van Veldhuizen finite difference method for solving a singular perturbation problem with layer behaviour. In this method, we introduce a fitting factor in Van Veldhuizen finite difference method to reduce the global error. The discrete invariant imbedding algorithm is used to solve the tridiagonal system.  This method controls the rapid changes that occur in the boundary layer region and it gives good results in both cases i.e., and.  We have presented maximum absolute errors for the standard examples chosen from the literature to describe the method.

Keywords: Singularly perturbed two point boundary value problem, Boundary layer, Tridiagonal matrix, diagonally dominant, Maximum absolute error.

 


International eJournal of Mathematics and Engineering

Volume 3, Issue 1, Pages:  1399 - 1410