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A Singularly Perturbed Reaction-Diffusion Problem with Incompatible Boundary-Initial Data

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Numerical Analysis and Its Applications (NAA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8236))

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Abstract

A singularly perturbed reaction-diffusion parabolic problem with an incompatibility between the initial and boundary conditions is examined. A finite difference scheme is considered which utilizes a special finite difference operator and a piecewise uniform Shishkin mesh. Numerical results are presented for both nodal and global pointwise convergence, using bilinear interpolation and, also, an interpolation method based on the error function. These results show that the method is not globally convergent when bilinear interpolation is used but they indicate that, for the test problem considered, it is globally convergent using the second type of interpolation.

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References

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Author information

Authors and Affiliations

  1. IUMA. Department of Applied Mathematics, University of Zaragoza, Spain

    J. L. Gracia & E. O’Riordan

  2. School of Mathematical Sciences, Dublin City University, Ireland

    J. L. Gracia & E. O’Riordan

Authors
  1. J. L. Gracia
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  2. E. O’Riordan
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Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technlogies, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl25A, 1113, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Pázm\’{a}ny P\’{e}ter s\’{e}t\’{a}ny 1/C,, Eötvös Loránd University, 1117, Budapest, Hungary

    István Faragó

  3. University of Rousse, 8 Studentska Str.,, 7017, Rousse, Bulgaria

    Lubin Vulkov

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Gracia, J.L., O’Riordan, E. (2013). A Singularly Perturbed Reaction-Diffusion Problem with Incompatible Boundary-Initial Data. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2012. Lecture Notes in Computer Science, vol 8236. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41515-9_33

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  • DOI: https://doi.org/10.1007/978-3-642-41515-9_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41514-2

  • Online ISBN: 978-3-642-41515-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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