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A fully adaptive approximation for quenching-type reaction-diffusion equations over circular domains



This article studies a fully adaptive finite difference method for solving quenching-type nonlinear reaction-diffusion equations over circular domains. Although an auxiliary condition at the origin and radial symmetry are imposed, adaptations are accomplished via arc-length-based monitoring functions in space and time, respectively. The monotonicity and positivity of the numerical solution are proved following a suitable grid constraint, and the numerical stability is ensured in the von Neumann sense. Theoretical bounds of the critical quenching radius are obtained and then refined through the computation. Computational examples are provided to illustrate the effectiveness and plausibility of the new adaptive computational procedure developed. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 472–489, 2014