To put more information into a difference scheme of a differentialequation for making an accurate prediction, a new kind of time integration scheme,known as the retrospective (RT) scheme, is proposed on the basis of the memorialdynamics. Stability criteria of the scheme for an advection equation in certain condi-tions are derived mathematically. The computations for the advection equation havebeen conducted with its RT scheme. It is shown that the accuracy of the scheme ismuch higher than that of the leapfrog (LF) difference scheme.
