A seventh order numerical method for singular perturbation problems

In this paper, a seventh order numerical method is presented for solving singularly perturbed two-point boundary value problems with a boundary layer at one end point. The two-point boundary value problem is transformed into general first order ordinary differential equation system. A discrete approximation of a seventh order compact difference scheme is presented for the first order system. An asymptotically equivalent first order equation of the original singularly perturbed two-point boundary value problem is obtained from the theory of singular perturbations. It is used in the seventh order compact difference scheme to get a two term recurrence relation and is solved. Several linear and nonlinear singular perturbation problems have been solved and the numerical results are presented to support the theory.