https://doi.org/10.1051/epjconf/201610802019
Adaptive WENO Schemes for Singular in Space and Time Solutions of Nonlinear Degenerate Reaction-Diffusion Problems
Faculty of Mathematics and Informatics, Sofia University “St. Kliment Ohridski”, Bulgaria
a e-mail: dimova@fmi.uni-sofia.bg
b e-mail: yonitamihaylova@yahoo.com
Published online: 9 February 2016
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.
© Owned by the authors, published by EDP Sciences, 2016
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.