Numerical integration method for general singularly perturbed two point boundary value problems

Abstract

In this paper, a numerical integration method is presented for solving general singularly perturbed two-point boundary value problems. The original second-order differential equation is replaced by an approximate first-order differential equation with a small deviating argument. Then, the trapezoidal formula is used to obtain the three-term recurrence relationship. The proposed method is iterative on the deviating argument. To demonstrate the applicability of the method, we have solved several model linear and non-linear examples with left-end boundary layer or right-end boundary layer or an internal layer or two boundary layers and presented the computational results.