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(tau(2) + h(2)) in the maximal norm based on an assumption of monotone initial data and smooth solutions, where tau is the temporal step size and h is the spatial step size. Finally, numerical experiments are applied to illustrate the effectiveness of theoretical results.