• Journal of applied mathematics & informatics
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• 제37권3_4호
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• pp.183-200
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• 2019

We have constructed a robust numerical method on Shishkin mesh for a class of convection diffusion type turning point problems with Robin type boundary conditions. Supremum norm is used to derive error estimates which is of order O($N^{-1}$ ln N). Theoretical results are verified by providing numerical examples.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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• pp.113-132
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• 2020

In this paper, a class of linear second order singularly perturbed delay differential turning point problems containing a small delay (or negative shift) on the reaction term and when the solution of the problem exhibits twin boundary layers are examined. A hybrid finite difference scheme on an appropriate piecewise-uniform Shishkin mesh is constructed to discretize the problem. We proved that the method is almost second order ε-uniformly convergent in the maximum norm. Numerical experiments are considered to illustrate the theoretical results.

• 대한수학회지
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• 제51권4호
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• pp.679-702
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• 2014

Investigation of the numerical solution of singularly perturbed turning point problems dates back to late 1970s. However, due to the presence of layers, not many high order schemes could be developed to solve such problems. On the other hand, one could think of applying the convergence acceleration technique to improve the performance of existing numerical methods. However, that itself posed some challenges. To this end, we design and analyze a novel fitted operator finite difference method (FOFDM) to solve this type of problems. Then we develop a fitted mesh finite difference method (FMFDM). Our detailed convergence analysis shows that this FMFDM is robust with respect to the singular perturbation parameter. Then we investigate the effect of Richardson extrapolation on both of these methods. We observe that, the accuracy is improved in both cases whereas the rate of convergence depends on the particular scheme being used.