Numerical Integration Method for Singular-Singularly Perturbed Two-Point Boundary Value Problems

In this paper, we proposed a numerical integration method for solving singular-singular perturbation two-point boundary value problems. The original boundary value problem is transformed to an asymptotically equivalent first order differential equation with a small deviating argument. A three term recurrence relation is obtained by applying Trapezoidal rule on the first order differential equation. At the singularity the original boundary value problem is modified. Then, we solved the three term recurrence relation by Thomas algorithm. To demonstrate the applicability of the method we have implemented it on several examples. Numerical results are compared with the exact solution to validate the method.