自忆模式中差分格式的稳定性研究

On the stability of the difference scheme in the self-memorization model

基于大气运动是一种不可逆过程的观点 ,引进了忆及过去时次资料的记忆函数 ,导出热传导的自忆性方程 ,研究了方程分别取Richardson和DuFort Frankel格式 ,回溯阶p取 1时的稳定性 .探讨了多时刻模式中数值积分有时发散的问题 ,揭示了由过去时次资料动态求取记忆函数 ,改变了原定设计的差分格式 ,且它是一个时间平滑因子的本质 .

In light of irreversibility of atmospheric motion, the memory function obtained by utilizing the previous information fully obtained from the observational data is introduced. The self-memorization equation of the heat conduction equation is induced, and the stability and characteristics of which are studied, taking respectively Richardson scheme (RS) and DuFort-Frankel scheme (DS) as the retrospective order p=1. The calculation results indicate that the numerical integral is diffused sometimes in the multi-time model, due to the fact that the memory function is determined by the observational data via the special mathematics arithmetic, which makes the difference scheme designed previously change, and is a smooth time factor in itself.