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

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.