An adaptive splitting approach for the quenching solution of reaction-diffusion equations over nonuniform grids

Authors:
Matthew A. Beauregard;Qin Sheng
Affiliations:
-;-
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

Citing 7
Cited 1

Remarks on quenching

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An adaptive Rothe method for nonlinear reaction-diffusion systems

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A splitting moving mesh method for reaction-diffusion equations of quenching type

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Numerical quenching for the semilinear heat equation with a singular absorption

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Solving degenerate quenching-combustion equations by an adaptive splitting method on evolving grids

Computers and Structures

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Abstract

The numerical solution of a nonlinear degenerate reaction-diffusion equation of the quenching type is investigated. While spatial derivatives are discretized over symmetric nonuniform meshes, a Peaceman-Rachford splitting method is employed to advance solutions of the semidiscretized system. The temporal step is determined adaptively through a suitable arc-length monitor function. A criterion is derived to ensure that the numerical solution acquired preserves correctly the positivity and monotonicity of the analytical solution. Weak stability is proven in a von Neumann sense via the ~-norm. Computational examples are presented to illustrate our results.