A note on the numerical-integration method for solving singular perturbation problems

摘要

The numerical-integration method recently proposed by Reddy for solving linear, singularly perturbed two-point boundary-value problems is investigated. The method was derived by approximating the original second-order problem with a first-order problem with a deviating argument, and then using Simpson's rule. It is shown here that, in the limit as the deviating argument tends to zero, the method converges to a one-sided difference approximation to the original problem in conservation form.