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Parameter-uniform numerical methods for some linear and nonlinear singularly perturbed convection diffusion boundary turning point problems

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Abstract

Both linear and nonlinear singularly perturbed two point boundary value problems are examined in this paper. In both cases, the problems have a boundary turning point and are of convection-diffusion type. Parameter-uniform numerical methods composed of monotone finite difference operators and piecewise-uniform Shishkin meshes, are constructed and analyzed for both the linear and the nonlinear class of problems. Numerical results are presented to illustrate the theoretical parameter-uniform error bounds established.

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Authors and Affiliations

  1. School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland

    E. O’Riordan & J. Quinn

Authors
  1. E. O’Riordan
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  2. J. Quinn
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Correspondence to E. O’Riordan.

Additional information

Communicated by Per Lötstedt.

This research was supported by the Irish Research Council for Science, Engineering and Technology.

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O’Riordan, E., Quinn, J. Parameter-uniform numerical methods for some linear and nonlinear singularly perturbed convection diffusion boundary turning point problems. Bit Numer Math 51, 317–337 (2011). https://doi.org/10.1007/s10543-010-0290-4

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  • DOI: https://doi.org/10.1007/s10543-010-0290-4

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