Abstract: A straightforward semi-implicit finite difference method approximating a system of conservation laws including a stiff relaxation term is analyzed. We show that the error, measured in $\Lone$, is bounded by $O(\sqrt{\dt})$ independent of the stiffness, where the time step $\dt$ represents the mesh size. Furthermore, we show that solutions of the stiff system converge towards the solution of an equilibrium model at a rate of $O(\delta^{1/3})$ in $\Lone$ as the relaxation time $\delta$ tends to zero.
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