Adaptive WENO Schemes for Singular in Space and Time Solutions of Nonlinear Degenerate Reaction-Diffusion Problems

Adaptive WENO Schemes for Singular in Space and Time Solutions of Nonlinear Degenerate Reaction-Diffusion Problems

The numerical solution of nonlinear degenerate reaction-diffusion problems often meets two kinds of difculties: singularities in space – finite speed of propagation of compact supports’ initial perturbations and possible sharp moving fronts, where the solution has low regularity, and singularities i...

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Main Authors: Dimova Stefka, Mihaylova Yonita
Format: Article
Language:English
Published: EDP Sciences 2016-01-01
Series:EPJ Web of Conferences
Online Access:http://dx.doi.org/10.1051/epjconf/201610802019
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spelling doaj-f8494951b94c486cb040c8ceb049ec342021-08-02T09:43:38ZengEDP SciencesEPJ Web of Conferences2100-014X2016-01-011080201910.1051/epjconf/201610802019epjconf_mmcp2016_02019Adaptive WENO Schemes for Singular in Space and Time Solutions of Nonlinear Degenerate Reaction-Diffusion ProblemsDimova Stefka0Mihaylova Yonita1Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”The numerical solution of nonlinear degenerate reaction-diffusion problems often meets two kinds of difculties: singularities in space – finite speed of propagation of compact supports’ initial perturbations and possible sharp moving fronts, where the solution has low regularity, and singularities in time – blow-up or quenching in finite time. We propose and implement a combination of the sixth-order WENO scheme of Liu, Shu and Zhang [SIAM J.Sci.Comput. 33, 939–965 (2011)] with an adaptive procedure to deal with these singularities. Numerical results on the mathematical model of heat structures are shown.http://dx.doi.org/10.1051/epjconf/201610802019
collection DOAJ
language English
format Article
sources DOAJ
author Dimova Stefka
Mihaylova Yonita
spellingShingle Dimova Stefka
Mihaylova Yonita
Adaptive WENO Schemes for Singular in Space and Time Solutions of Nonlinear Degenerate Reaction-Diffusion Problems
EPJ Web of Conferences
author_facet Dimova Stefka
Mihaylova Yonita
author_sort Dimova Stefka
title Adaptive WENO Schemes for Singular in Space and Time Solutions of Nonlinear Degenerate Reaction-Diffusion Problems
title_short Adaptive WENO Schemes for Singular in Space and Time Solutions of Nonlinear Degenerate Reaction-Diffusion Problems
title_full Adaptive WENO Schemes for Singular in Space and Time Solutions of Nonlinear Degenerate Reaction-Diffusion Problems
title_fullStr Adaptive WENO Schemes for Singular in Space and Time Solutions of Nonlinear Degenerate Reaction-Diffusion Problems
title_full_unstemmed Adaptive WENO Schemes for Singular in Space and Time Solutions of Nonlinear Degenerate Reaction-Diffusion Problems
title_sort adaptive weno schemes for singular in space and time solutions of nonlinear degenerate reaction-diffusion problems
publisher EDP Sciences
series EPJ Web of Conferences
issn 2100-014X
publishDate 2016-01-01
description The numerical solution of nonlinear degenerate reaction-diffusion problems often meets two kinds of difculties: singularities in space – finite speed of propagation of compact supports’ initial perturbations and possible sharp moving fronts, where the solution has low regularity, and singularities in time – blow-up or quenching in finite time. We propose and implement a combination of the sixth-order WENO scheme of Liu, Shu and Zhang [SIAM J.Sci.Comput. 33, 939–965 (2011)] with an adaptive procedure to deal with these singularities. Numerical results on the mathematical model of heat structures are shown.
url http://dx.doi.org/10.1051/epjconf/201610802019
work_keys_str_mv AT dimovastefka adaptivewenoschemesforsingularinspaceandtimesolutionsofnonlineardegeneratereactiondiffusionproblems
AT mihaylovayonita adaptivewenoschemesforsingularinspaceandtimesolutionsofnonlineardegeneratereactiondiffusionproblems
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