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

In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems 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 perturbation parameter. Several problems are solved and numerical results are presented to support the theoretical error bounds established.