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

✍ Scribed by Edgardo A. Moyano; Alberto F. Scarpettini

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 417 KB
Volume: 16
Category: Article
ISSN: 0749-159X
DOI: 10.1002/(sici)1098-2426(200001)16:1<42::aid-num4>3.0.co;2-l

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✦ Synopsis

Two algorithms are described [Ferris D. H. (fixed time-step method) and Gupta and Kumar (variable timestep 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.