A numerical method for a free boundary value problem arising from chemical kinetics
type: Item
instance of: scholarly article
title: A numerical method for a free boundary value problem arising from chemical kinetics
zbMATH Open document ID: 1083.65515
DOI: 10.1016/S0377-0427(99)00142-9
author: Nicholas Batens
author: Roger Van Keer
published in: Journal of Computational and Applied Mathematics
publication date: 1999-01-01T00:00:00Z
review text: In this paper we deal with a numerical method for a complex free boundary value problem (FBP) in 1D, arising from chemical kinetics and involving two moving internal boundary points and six unknown concentration profiles. Basically, the method consists of three steps: (1) a suitable fixed domain transformation for each of the three time-varying intervals, which results in a strongly nonlinear, nonlocal boundary value problem (BVP); (2) a nonstandard central difference method with respect to the space variable, that takes properly into account the various transition conditions, in particular by using quadratic Lagrange interpolation to approximate the involved concentration profiles near the relevant grid points; (3) a time discretisation method for the resulting initial value problem (IVP) for the nonlinear system of 1st order ODEs, that takes fully profit of the special structure of the mass matrix, implying that only a full \(8\times 8\) submatrix must be inverted at each discrete time point. A numerical example is presented.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 80A30
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 1398829
zbMATH Keywords: Free boundary problem
zbMATH Keywords: Fixed domain transformation
zbMATH Keywords: Nonlinear and nonlocal boundary value problem
zbMATH Keywords: Linear system of ODEs
describes a project that uses: ODEPACK
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1398829