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Some Features of the Asymptotic-Numerical Method for the Moving Fronts Description in Two-Dimensional Reaction-Diffusion Problems

  • Vladimir VolkovEmail author
  • Dmitry Lukyanenko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

This paper develops an analytic-numerical approach for the description of moving fronts in two-dimensional nonlinear singularly perturbed parabolic equations. Asymptotic technique allows to reduce two-dimensional nonlinear reaction-diffusion equation to a series of more simple one-dimensional problems. This decomposition significantly decreases the complexity of numerical calculations and allows the effective use of parallel computing. Some numerical experiments are presented to demonstrate the main features of the proposed method.

Notes

Acknowledgements

This work is supported by RSCF, project No. 18-11-00042.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of PhysicsLomonosov Moscow State UniversityMoscowRussia

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