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Parameter-uniform numerical methods for some singularly perturbed nonlinear initial value problems

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Abstract

Parameter-uniform numerical methods for singularly perturbed nonlinear scalar initial value problems are both constructed and analysed in this paper. The conditions on the initial condition for a stable initial layer to form are identified. The character of a stable initial layer in the vicinity of a double root of the reduced algebraic problem is different to the standard layer structures appearing in the neighbourhood of a single stable root of the reduced problem. Results for a problem where two reduced solutions intersect are also discussed. Numerical results are presented to illustrate the theoretical results obtained.

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References

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Authors and Affiliations

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

    Eugene O’Riordan & Jason Quinn

Authors
  1. Eugene O’Riordan
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  2. Jason Quinn
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Correspondence to Eugene O’Riordan.

Additional information

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 singularly perturbed nonlinear initial value problems. Numer Algor 61, 579–611 (2012). https://doi.org/10.1007/s11075-012-9552-3

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  • DOI: https://doi.org/10.1007/s11075-012-9552-3

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