An efficient numerical method for singularly perturbed second order ordinary differential equation

Abstract. In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value prob- lems with the boundary layer. A fitting factor is introduced and the model equation is discretized by a finite difference scheme on an uniform mesh. Thomas algorithm is used to solve the tri-diagonal system. The stability of the algorithm is investigated. It is shown that the proposed technique is of first order accurate and the error constant is independent of the pertur- bation parameter. Several problems are solved and numerical results are presented to support the theoretical error bounds established.