Abstract
In this paper, an extended mixed asymptotic-numerical method is presented for a one dimensional two point singularly perturbed boundary value problem. The original problem is solved separately on outer and inner region. The outer region problem called the reduced problem is solved using the q-stage Runge-Kutta method and the inner region problem is solved asymptotically. A uniform error estimate of $$\mathcal {O}(h^p),$$ $$(p\le q)$$ is obtained. Several numerical examples are taken to illustrate the comparative study. The method is also extended to delay and advance problem.
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