Abstract
In this paper we establish error bounds for a finite-difference approximation to solutions of certain parabolic systems of the form ${v_t} + f{(v)_x} = \varepsilon {v_{xx}}$. We assume that the Cauchy data is of class BV, and we show that the sup norm of the error is bounded by $O(\Delta x|\ln \Delta x|)$ at positive times.
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