Abstract
To put more information into a difference scheme of a differential equation 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 memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme.
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The project supported by the National Key Program for Developing Basic Sciences (G1999043408 and G1998040901-1) and the National Natural Sciences Foundation of China (40175024 and 40035010)
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Guolin, F., Wenjie, D., Peicai, Y. et al. Retrospective time integral scheme and its applications to the advection equation. Acta Mech Sinica 18, 53–65 (2002). https://doi.org/10.1007/BF02487524
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DOI: https://doi.org/10.1007/BF02487524