Abstract
In this paper we are concerned with the numerical integration of Burgers equation backward in time. We construct a one-step backward group preserv- ing scheme (BGPS) for the semi-discretization of Burg- ers equation. The one-step BGPS is very effectively to calculate the solutionat an initial timet = 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 ac- curate solution never seen before. Under noisy final data the BGPS is also robust to againstthe disturbance. When the solution appears steep gradient, several steps BGPS can be used to retrieve the desired initial data. keyword: Past cone dynamics, Backward group pre- serving scheme, Backward Burgers equation, Ill-posed
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