### A derivative array approach for linear second order differential-algebraic systems.

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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...

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...