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

摘要

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.