An implicit scheme to solve a system of ODEs arising from the space discretization of nonlinear diffusion equations
Department of Mathematics, EPFL, 1015 Lausanne, Switzerland. (firstname.lastname@example.org)
Revised: 12 February 2001
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.
Mathematics Subject Classification: 65L05 / 65L80 / 65N30
Key words: Nonlinear diffusion equations / nonlinear parabolic problem / Chernoff scheme / implicit scheme for ODE's.
© EDP Sciences, SMAI, 2001