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

Matthew A. Beauregard, Qin Sheng

• 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.