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A System of Singularly Perturbed Semilinear Equations

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BAIL 2008 - Boundary and Interior Layers

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 69))

Abstract

In this paper systems of singularly perturbed semilinear reaction-diffusion equations are examined. A numerical method is constructed for these systems which involves an appropriate layer-adapted piecewise-uniform mesh. The numerical approximations generated from this method are shown to be uniformly convergent with respect to the singular perturbation parameters.

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References

  1. J.L. Gracia, F.J. Lisbona, E. O'Riordan, A system of singularly perturbed reaction-diffusion equations, Dublin City University School of Mathematical Sciences preprint MS-07-10, (2007).

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  2. J.L. Gracia, F.J. Lisbona, M. Madaune-Tort, E. O'Riordan, A coupled system of singularly perturbed semilinear reaction-diffusion equations, Dublin City University School of Mathematical Sciences Preprint, MS-08-11, (2008).

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  3. J.L. Gracia, F.J. Lisbona, E. O'Riordan, A coupled system of singularly perturbed parabolic reaction-diffusion equations. Adv. Comp. Math., DOI 10.1007/s10444-008-9086-3.

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  4. T. Linß, N. Madden, Accurate solution of a system of coupled singularly perturbed reaction-diffusion equations, Computing, 73 (2004), 121–133.

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  5. T. Linß, N. Madden, Layer-adapted meshes for a system of coupled singularly perturbed reaction-diffusion equations, IMA J. Numer. Anal., 29(2009), 109–125.

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  6. N. Madden, M. Stynes, A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction-diffusion problems, IMA J. Numer. Anal., 23 (2003) 627–644.

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Author information

Authors and Affiliations

  1. Departamento de Matemática Aplicada, Universidad de Zaragoza, Zaragoza, Spain

    J. L. Gracia, F. J. Lisbona, M. Madaune-Tort & E. O’Riordan

Authors
  1. J. L. Gracia
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  2. F. J. Lisbona
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  3. M. Madaune-Tort
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  4. E. O’Riordan
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Corresponding author

Correspondence to J. L. Gracia .

Editor information

Editors and Affiliations

  1. Dept. Mathematics & Statistics, University of Limerick, Limerick, Ireland

    Alan Hegarty

  2. Dept. Mathematics & Statistics, University of Limerick, Limerick, Ireland

    Natalia Kopteva

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

    Eugene O'Riordan

  4. Dept. Mathematics, University College Cork, Aras Na Laoi , Cork, Ireland

    Martin Stynes

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© 2009 Springer-Verlag Berlin Heidelberg

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Gracia, J.L., Lisbona, F.J., Madaune-Tort, M., O’Riordan, E. (2009). A System of Singularly Perturbed Semilinear Equations. In: Hegarty, A., Kopteva, N., O'Riordan, E., Stynes, M. (eds) BAIL 2008 - Boundary and Interior Layers. Lecture Notes in Computational Science and Engineering, vol 69. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00605-0_12

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