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Front Dynamics in an Activator-Inhibitor System of Equations

  • Alina MelnikovaEmail author
  • Natalia Levashova
  • Dmitry Lukyanenko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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.

Keywords

Saddle Point Transition Layer Asymptotic Approximation Uniform Mesh Regular Part 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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.

Supplementary material

Supplementary material 1 (mp4 282 KB)

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Alina Melnikova
    • 1
    Email author
  • Natalia Levashova
    • 1
  • Dmitry Lukyanenko
    • 1
  1. 1.Faculty of Physics, Department of MathematicsLomonosov Moscow State UniversityMoscowRussia

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