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
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
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