A monotone iterative method for numerical solution of diffusion equations with nonlinear localized chemical reactions

Authors:
Juri D. Kandilarov
Affiliations:
Center of Applied Mathematics and Informatics, University of Rousse, Rousse, Bulgaria
Venue:
NMA'06 Proceedings of the 6th international conference on Numerical methods and applications
Year:
2006

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Abstract

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.