Error bounds for finite-difference approximations for a class of nonlinear parabolic systems

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 = ε v x x {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 ( Δ x | ln ⁡ Δ x | ) O(\Delta x|\ln \Delta x|) at positive times.