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A multi region finite difference method is described and applied to the one dimension, semi linear, singularly perturbed boundary value problem (SPBVP). The process of developing high precision algorithms for this problem is described and it is shown that when the multi region method is combined with the use of these high order algorithms, numerical solutions can achieve accuracies in the range of...
Singularly perturbed ordinary differential equation with two small parameters is considered. Firstly, the solution is decomposed into the smooth component and the singular component. The upper bounds of the smooth component and the singular component are studied. Secondly, the traditional Shishkin's scheme is presented and it is proved to be uniformly convergent with respect to the small parameter...
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