Numerical stability study and error estimation for two implicit schemes in a moving boundary problem

Two algorithms are described [Ferris D. H. (fixed time‐step method) and Gupta and Kumar (variable time‐step method)] that solve a mathematical model for the study of the one‐dimensional moving boundary problem with implicit boundary conditions. Landau's transformation is used, in order to work...

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Bibliographic Details
Published inNumerical methods for partial differential equations Vol. 16; no. 1; pp. 42 - 61
Main Authors Moyano, Edgardo A., Scarpettini, Alberto F.
Format Journal Article
LanguageEnglish
Published New York John Wiley & Sons, Inc 01.01.2000
Subjects
diffusion-convection
moving boundary
nonlinear
nonlinear, parabolic
numerical stability
parabolic
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Summary:Two algorithms are described [Ferris D. H. (fixed time‐step method) and Gupta and Kumar (variable time‐step method)] that solve a mathematical model for the study of the one‐dimensional moving boundary problem with implicit boundary conditions. Landau's transformation is used, in order to work with a fixed number of nodes at each time‐step. The p.d.e. is discretized using an implicit finite difference scheme. The mathematical model describes the oxygen diffusion in absorbing tissues. An important application is the estimation of time‐variant radiation treatments of cancerous tumors. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 42–61, 2000
Bibliography:istex:A7DBDF67392CF7021DF716902F217512A873A3B7
ark:/67375/WNG-VKMKJ4VM-P
ArticleID:NUM4
ISSN:0749-159X
1098-2426
DOI:10.1002/(SICI)1098-2426(200001)16:1<42::AID-NUM4>3.0.CO;2-L