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

摘要

In this paper, a fitted fourth-order tridiagonal finite difference scheme is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. We have taken a fourth-order tridiagonal finite difference scheme by M.M. Chawla [A fourth-order tridiagonal finite difference method for general nonlinear two-point boundary value problems with mixed boundary conditions, J. Inst. Maths Appl. 21 (1978) 83–93] and introduced a fitting factor. The fitting factor is obtained from the theory of singular perturbations. Thomas Algorithm is used to solve the system. To demonstrate the applicability of the present method, we have solved five linear problems (three with left end and two with right end boundary layers). Solutions of these problems using the present fitted method are compared with Chawla’s solutions. From the results, it is observed that the present method is stable and has better approximation to the exact solution.