Abstract
A new way to solve singular perturbation problems is introduced. It is designed for the practicing engineer or applied mathematician who needs a practical tool for these problems (easy to use, modest problem preparation and ready computer implementation). In this paper, we consider singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) point. An initial-value technique is used for its solution. However, this technique is based on the boundary layer behavior of the solution. It is distinguished by the following fact: The original second order problem is replaced by an asymptotically equivalent first-order problem and is solved as an initial-value problem via cubic spline. Numerical experience with several linear and non-linear examples is described. It is observed that the present method approximates the exact solution very well.
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