An exponentially fitted non symmetric finite difference method for singular perturbation problems

Abstract

In this paper, we have presented an exponentially fitted non symmetric numerical method for singularly perturbed differential equations with layer behaviour. We have introduced a fitting factor in a non symmetric finite difference scheme which takes care of the rapid changes occur that in the boundary layer. This fitting factor is obtained from the theory of singular perturbations. The discrete invariant imbedding algorithm is used to solve the tridiagonal system of the fitted method. This method controls the rapid changes that occur in the boundary layer region and it gives good results in both cases i.e., h ≤ ε and ε << h. The existence and uniqueness of the discrete problem along with stability estimates are discussed. Also we have discussed the convergence of the method. Maximum absolute errors in numerical results are presented to illustrate the proposed method for ε << h.