A nonasymptotic method for singular perturbation problems

In this paper, an approximate method for the numerical integration of singularly perturbed two-point boundary-value problems with a boundary layer on the left end of the underlying interval is presented. The method is distinguished by the following fact: the original second-order differential equation is replaced by an approximate first-order differential equation with a small deviating argument and is solved efficiently by employing the Simpson rule, coupled with the discrete invariant imbedding algorithm. The proposed method is iterative on the deviating argument. Several numerical examples have been solved to demonstrate the applicability of the method.