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针对■ζ/■_t+u■ζ/■_x=0方程,本文首先讨论了在一般情形下所谓“先向前差、后中央差”差分格式的稳定性,并给出了稳定的条件。其结果和一般只用中央差分的情形有所不同。利用三种差分格式进行比较,发现目前广泛应用的用向前差计算第一个时间步长,以后全用中央差的格式是最差的;当λ(=uΔt/Δs)→1—0时,计算并不稳定。如果用另两种格式中任一种代替向前差,则可以避免这个困难。其中又以“逆2—3格式”较好。
In this paper, we first discuss the stability of the so-called “difference-first-difference-difference-before-difference” difference scheme in general, and give the conditions for the stabilization of ζ / ■ _t + u ■ ζ / ■ _x = 0 equations. The result is somewhat different from the one that normally uses only the central difference. It is found that the first time step is widely used to calculate the first time step, and then the format with the worst center difference is the worst. When λ (= uΔt / Δs) → 1-0 , Calculation is not stable. This difficulty can be avoided if one of the other two formats is used instead of the forward difference. Which again “inverse 2-3 format” is better.