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An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations

Published online by Cambridge University Press:  15 April 2002

Éric Boillat
Éric Boillat*
Affiliation:
Department of Mathematics, EPFL, 1015 Lausanne, Switzerland. ([email protected])
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Abstract

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.

Keywords

Nonlinear diffusion equationsnonlinear parabolic problemChernoff schemeimplicit scheme for ODE's.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 35 , Issue 4 , July 2001 , pp. 749 - 765
Copyright
© EDP Sciences, SMAI, 2001

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