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On some difference schemes for singular singularly-perturbed boundary value problems

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Summary

Singularly perturbed boundary value ordinary differential problems are considered, where the problem defining the reduced solution is singular. For numerical approximation, families of symmetric difference schemes, which are equivalent to certain collocation schemes based on Gauss and Lobatto points, are used. Convergence results, previously obtained for the “regular” singularly perturbed case, are extended. While Gauss schemes are extended with no change, Lobatto schemes require a small modification in the mesh selection procedure. With meshes as prescribed in the text, highly accurate solutions can be obtained with these schemes for singular singularly perturbed problems at a very reasonable cost. This is demonstrated by examples.

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Authors and Affiliations

  1. Department of Computer Science, The University of British Columbia, V6T 1W5, Vancouver, Canada

    Uri Ascher

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  1. Uri Ascher
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This research was completed while the author was visiting the Department of Applied Mathematics, Weizmann Inst., Rehovot, Israel. The author was supported in part under NSERC grant A4306

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Ascher, U. On some difference schemes for singular singularly-perturbed boundary value problems. Numer. Math. 46, 1–30 (1985). https://doi.org/10.1007/BF01400252

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