摘要
提出了"开关"问题的一类微分方程模型,方程在临界值处是不连续的.用经典的数值方法求解此类问题时会出现很大的数值误差,数值精度降到了一阶.详细研究了这类问题,提出用Hermite插值方法确定开关时刻,分段求解连续的微分方程的间断装配方法,使原有的数值方法恢复其数值精度.将此方法应用到资料变分同化中,获得了高精度的数值解.
A general discontinuous ODE model is presented which describe parameterize physical process in numerical weather forecasting. Classical methods such as Runge-Kutta scheme can't hold their ordinarily high precision because of discontinuity. A discontinuity fitting method is proposed by using Hermite interpolation to catch discontinuous point and treating different zonal with classical methods, respectively. New method is applied to variational data assimilation and can reach its high precision globally.
出处
《科技通报》
北大核心
2003年第5期417-420,共4页
Bulletin of Science and Technology
关键词
计算数学
间断
开关
装配
资料变分同化
精度
computational mathematics
numerical analysis
on-off, discontinuity, discontinuity fitting, data assimilation, precision
