Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approximations

Summary A method for improvement of the numerical solution of differential equations by incorporation of asymptotic approximations is investigated for a class of singular perturbation problems.Uniform error estimates are derived for this method when implemented in known difference schemes and applied to linear second order O.D.E.'s. An improvement by a factor ofⁿ⁺¹ can be obtained (where is the small parameter andn is the order of the asymptotic approximation) for a small amount of extra work. Numerical experiments are presented.