A new difference scheme with multi-time levels

摘要

In view of making the best use of information coming from past observational data, a new difference scheme with multi-time levels (p＞3) is suggested. Some mathematical characteristics of the scheme, which is called the retrospective scheme, are discussed. The numerical results of some examples show that the calculation accuracy of linear and nonlinear advection equations computed with the retrospective scheme is higher than that obtained via the leapfrog scheme. The scheme can be applied to many fields, such as meteorology, engineering physics, astronautics, environment and economy etc, where systematic observations are made normally.