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.
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This work is supported by RSCF, project No. 18-11-00042.
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Volkov, V., Lukyanenko, D. (2019). Some Features of the Asymptotic-Numerical Method for the Moving Fronts Description in Two-Dimensional Reaction-Diffusion Problems. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_72
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DOI: https://doi.org/10.1007/978-3-030-11539-5_72
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