Fourth Order Fitted Scheme for Second Order Singular Perturbation Boundary Value Problems

Fitted fourth order central difference scheme is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end point. A fitting factor is introduced in a tri-diagonal finite difference scheme and is obtained from the theory of singular perturbations. Thomas Algorithm is used to solve the system and its stability is investigated. To demonstrate the applicability of the method, we have solved linear and nonlinear problems. From the results, it is observed that the present method approximates the exact solution very well.