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International Conference on Numerical Analysis and Its Applications

NAA 2016: Numerical Analysis and Its Applications pp 492–499Cite as

Front Dynamics in an Activator-Inhibitor System of Equations

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10187))

Abstract

We consider the construction of formal asymptotic approximation for solution of the singularly perturbed boundary value problem of an activator-inhibitor type with a solution in a form of moving front. Corresponding asymptotic analysis provides a priori information about the localization of the transition point for moving front that is further used for constructing of dynamic adapted mesh. This mesh significantly improves numerical stability of numerical calculations for the considered system.

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References

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Acknowledgements

This study was supported by grants of the Russian Foundation for Basic Research projects No. 16-01-00437, 15-01-04619 and 16-01-00755.

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Authors and Affiliations

  1. Faculty of Physics, Department of Mathematics, Lomonosov Moscow State University, Moscow, 119991, Russia

    Alina Melnikova, Natalia Levashova & Dmitry Lukyanenko

Authors
  1. Alina Melnikova
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  2. Natalia Levashova
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  3. Dmitry Lukyanenko
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Corresponding author

Correspondence to Alina Melnikova .

Editor information

Editors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Ivan Dimov

  2. Department of Applied Analysis, Eötvös Loránd University, Budapest, Hungary

    István Faragó

  3. Department of Applied Mathematics and Statistics, University of Rousse, Ruse, Bulgaria

    Lubin Vulkov

1 Electronic supplementary material

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Supplementary material 1 (mp4 282 KB)

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Melnikova, A., Levashova, N., Lukyanenko, D. (2017). Front Dynamics in an Activator-Inhibitor System of Equations. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Numerical Analysis and Its Applications. NAA 2016. Lecture Notes in Computer Science(), vol 10187. Springer, Cham. https://doi.org/10.1007/978-3-319-57099-0_55

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  • DOI: https://doi.org/10.1007/978-3-319-57099-0_55

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57098-3

  • Online ISBN: 978-3-319-57099-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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