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Fitted sixth-order tridiagonal finite difference method for singular perturbation problems

K. Phaneendraa , Y.N. Reddy b and GBSL.Soujanya c

a,b,c Department of mathematics, National Institute of  Technology

 

Abstract

       In this paper, a fitted sixth-order tridiagonal finite difference scheme is presented for solving singularly perturbed two point boundary value problems with the boundary layer at one end point.  We consider a six-order tridiagonal finite difference scheme by M.M. Chawla [A sixth-order Tridiagonal Finite Difference Method for General Non-linear Two-point Boundary Value Problems, J.Inst. Maths Appl. 24 (1979), 35-42] and introduced a fitting factor.  The fitting factor is obtained from the theory of singular perturbations.  Thomas algorithm is used to solve the tridiagonal system.  To demonstrate the applicability of the present method, we have solved five linear problems three with left and two with right end boundary layers.  Solutions of these problems using the present fitted method are compared with Chawla’s solutions.  From the numerical results, it is observed that the present method is stable and has better approximation to the exact solution.

Keywords:  Singular perturbation problems; Boundary layer; Finite differences; Fitted method

 

 


International eJournal of Mathematics and Engineering

Volume 3, Issue 1, Pages:  1338 - 1351