变步长显式完全平方守恒差分格式

A SPECIES OF EXPLICIT COMPLETE SQUARE CONSERVATIVE DIFFERENCE SCHEMES WITH ADJUSTABLE TIME STEP INTERVALS

综合隐式完全平方守恒差分格式和显式瞬时平方守恒差分格式的优点，针对一类非线性发展方程构造了一种通过自动调节时间步长来保持平方守恒性的显式差分格式。它基于加小耗散的思想，但又与小耗散法有所不同。本文取的耗散项不是一般的人工耗散，而是取能够弥补由于时间离散所产生的截断误差的所谓（时间）协调耗散。因此，该格式具有较高的时间精度。在数值试验中，该类格式可取得满意的效果。

n this paper. a kind of explicit difference schemes to solve nonlinear evolution equations. Perfectly keeping the Square conservation by adjusting the time step interval, is constructed. from the comprehensive maintenance of the advantages of the implicit complete square conservative scheme and the explicit instantaneous square conservative scheme. The new schemes are based on the thought of adding a small dissipation, but it is different from the Small dissipation Method. The dissipative term used in the new schemes is not a simple artificial dissipative term. It is a so-called (time) consistent dissipative term that can compensate for the truncation errors from the dissociation of the time differential term. Therefore, the new schemes may have a high time precision and may acquire a satisfactory effect in numerical tests.