A Monotone Iterative Method for Numerical Solution of Diffusion Equations with Nonlinear Localized Chemical Reactions

摘要

We study the numerical solution of a model two-dimensional problem, where the nonlinear reaction takes place only at some interface curves, due to the present of catalyst. A finite difference algorithm, based on a monotone iterative method and the immersed interface method (IIM), is proposed and analyzed. Our method is efficient with respect to flexibility in dealing with the geometry of the interface curve. The numerical results indicate first order of accuracy.