Modified arc-length adaptive algorithms for degenerate reaction-diffusion equations

Authors:
Q. Sheng;A. Q. M. Khaliq
Affiliations:
Department of Mathematics, University of Dayton, Dayton, OH;Department of Mathematics, Western Illinois University, Macomb, IL
Venue:
Applied Mathematics and Computation
Year:
2002

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Abstract

This paper is concerned with modified adaptive difference schemes for solving degenerate nonlinear reaction-diffusion equations with singular source terms. The adaptive mechanisms both in space and time are considered. Modified monitor functions based on arc-lengths of the rate function ut are constructed. Further analyses are given on properties of the numerical schemes derived. We show that, under proper smoothness, consistency and step-size constraints, the numerical solution obtained preserves the monotonicity of the physical solution. Numerical experiments are given to demonstrate the monotonicity and convergence properties of the methods.