On the monotonicity of an adaptive splitting scheme for two-dimensional singular reaction-diffusion equations

Authors:
Abdul Q. M. Khaliq;Qin Sheng
Affiliations:
Department of Mathematical Sciences, Middle Tennessee State University Murfreesboro, TN, USA;CASPER and Department of Mathematics, Baylor University Waco, TX, USA
Venue:
International Journal of Computer Mathematics - Splitting Methods for Differential Equations
Year:
2007

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Abstract

This paper studies a fully adaptive splitting method for the numerical solution of two-dimensional quenching differential equations. The non-uniform adaptive mesh is established in space and time via standard arc-length formulations. We concentrate on the monotonic property of the numerical algorithm developed since the issue is fundamental for this type of nonlinear singular differential equations. Numerical examples are given to illustrate our computational results as well as the quenching phenomena approximated.