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

• Autores: Matthew A. Beauregard, Qin Sheng
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 241, Nº 1, 2013, págs. 30-44
• Idioma: inglés
• DOI: 10.1016/j.cam.2012.10.005
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• Resumen

  • 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.