Numerical solution of singularly perturbed two point boundary value problems using exponentially fitted finite difference scheme

摘要

A computational method to solve linear as well as quasi-linear singularly perturbed two point boundary value problems having a boundary layer at one end point is presented. A fitted factor is introduced in the tridiagonal system by using the asymptotic solution of the problem. The system is solved by using the well-known Thomas algorithm. The stability and uniform convergence analysis of the method is also presented. To demonstrate the applicability of the method several examples have been considered. The maximum absolute errors for the problems without fitting factor and with fitting factor are compared in the tables. From the results it is clear that the presented method has a good approximation to the exact solution.