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Difference Methods for Quasilinear 2D‐diffusion Problems in Toroidal Configurations
Author(s) -
Finckenstein K. Graf Finck v.,
Forkel H.
Publication year - 1997
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199704)20:6<477::aid-mma844>3.0.co;2-x
Subject(s) - mathematics , convergence (economics) , space (punctuation) , diffusion , mathematical analysis , nonlinear system , boundary value problem , inverse , finite difference , toroid , plasma , geometry , physics , quantum mechanics , economics , thermodynamics , economic growth , linguistics , philosophy
Implicit one‐step difference methods for quasilinear parabolic initial boundary value problems in two space variables and in polar coordinates are considered. Problems of this kind are suitable for the description of diffusion processes in plasma physics. Therefore, because of its special physical interest the dependence of the coefficients both on the solution and on its space derivatives (the fluxes) is included. The first part of this paper deals with proving convergence of the discrete approximations for vanishing step sizes. For this purpose, bounds for the inverse difference operators have to be derived previously. The nonlinear systems arising from the discretizations have exactly one solution for all step sizes being sufficiently small. In the second part of the article numerical tests are performed. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.