An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
Boillat, Éric
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 35 (2001), p. 749-765 / Harvested from Numdam
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In this article, we consider the initial value problem which is obtained after a space discretization (with space step h) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size h chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between h and the time step size τ. Moreover, it is not of excessive algorithmic complexity since it does not require more than one resolution of a linear system at each time step.

Publié le : 2001-01-01
Classification:  65L05,  65L80,  65N30 
@article{M2AN_2001__35_4_749_0,
     author = {Boillat, \'Eric},
     title = {An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {35},
     year = {2001},
     pages = {749-765},
     mrnumber = {1863278},
     zbl = {0991.65091},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_2001__35_4_749_0}
}

Boillat, Éric. An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 35 (2001) pp. 749-765. http://gdmltest.u-ga.fr/item/M2AN_2001__35_4_749_0/

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