Kandilarov, Juri D.; Vulkov, Lubin G. The immersed interface method for a nonlinear chemical diffusion equation with local sites of reactions. (English) Zbl 1074.65102 Numer. Algorithms 36, No. 4, 285-307 (2004). The paper deals with the second-order accurate immersed interface method to solve the diffusion equation with nonlinear localized chemical reactions, i.e., the diffusion equation involving interfaces. This new method is more accurate than the standard approach and it does not require the interface to be grid points. Several experiments that confirm second-order accuracy and to solve blow up problems are presented. Reviewer: Marek Brandner (Plzeň) Cited in 14 Documents MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35K57 Reaction-diffusion equations 80A32 Chemically reacting flows 80M20 Finite difference methods applied to problems in thermodynamics and heat transfer Keywords:immersed interface method; nonlinear parabolic problems; finite difference schemes; numerical examples; diffusion equation; chemical reactions; blow up PDFBibTeX XMLCite \textit{J. D. Kandilarov} and \textit{L. G. Vulkov}, Numer. Algorithms 36, No. 4, 285--307 (2004; Zbl 1074.65102) Full Text: DOI References: [1] J.H. Ahlbery and E.H. Nilson, Convergence properties of the spline fit, J. SIAM 11 (1963) 95-104. · Zbl 0196.48701 [2] N.S. Bakhvalov, Numerical Methods (Nauka, Moscow, 1973). · Zbl 0254.41013 [3] R.P. Beyer and R.J. Leveque, Analysis of a one-dimensional model for the immersed boundary method, SIAM J. Numer. Anal. 29 (1992) 332-364. · Zbl 0762.65052 [4] K. 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