An efficient backward group preserving scheme for the backward in time Burgers equation

In this paper we are concerned with the numerical integration of Burgers equation backward in time. We construct a one-step backward group preserving scheme (BGPS) for the semi-discretization of Burgers equation. The one-step BGPS is very effectively to calculate the solution at an initial time t = 0 from a given final data at t = T, which with a time stepsize equal to T and with a suitable grid length produces a highly accurate solution never seen before. Under noisy final data the BGPS is also robust to against the disturbance. When the solution appears steep gradient, several steps BGPS can be used to retrieve the desired initial data.