A three-level implicit difference scheme for solving the inviscid Burgers' equation with time delay.

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 O (τ 2 + h 2) 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. [ABSTRACT FROM AUTHOR]