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Accessible Unlicensed Requires Authentication Published by De Gruyter August 7, 2015

Blow-up numerical solutions for a convective reaction–diffusion equation

Chia-Feng Chang, Yi-Chien Wu and Chien-Hong Cho

Abstract

We consider finite difference solutions of the 1-dimconvective reaction-diffusion equation ut = uxx + ɑ(um)x+uβ (ɑ > 0, β > m ≥ 1),whose solutions are known to become unbounded in finite time. To reproduce the finite-time blow-up phenomenon numerically, the temporal grid sizes are defined adaptively.We shownot only that our numerical solution blows up in finite time but also that the numerical blow-up time converges to the blow-up time of the PDE. In addition, we also investigate the behavior of the numerical solutions. Our numerical solutions reproduce certain significant blow-up properties of the continuous solutions.

Received: 2013-11-13
Accepted: 2014-3-3
Published Online: 2015-8-7
Published in Print: 2015-6-1

© 2015 by Walter de Gruyter Berlin/Boston