Abstract
A three-level implicit difference scheme is developed for a inviscid Burgers' equation with time delay. It is proved that the proposed scheme is uniquely solvable, stable, and unconditionally convergent with order in the maximal norm based on an assumption of monotone initial data and smooth solutions, where τ is the temporal step size and h is the spatial step size. Finally, numerical experiments are applied to illustrate the effectiveness of theoretical results.
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