Interval of effective time-step size for the numerical computation of nonlinear ordinary differential equations

The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the interval of effective step size（IES） has not been thoroughly explored theoretically.In this paper,by using a general estimation for the total error of the numerical solutions of ODEs,a method is proposed for determining an approximate IES by translating the functions for truncation and rounding errors.It also illustrates this process with an example.Moreover,the relationship between the IES and its approximation is found,and the relative error of the approximation with respect to the IES is given.In addition,variation in the IES with increasing integration time is studied,which can provide an explanation for the observed numerical results.The findings contribute to computational step-size choice for reliable numerical solutions.

“粒度分析法”在小流域泥沙来源研究中的应用

小流域泥沙来源是土壤侵蚀研究的重点内容 ,目前 ,国内外主要利用径流泥沙资料 ,采用统计分析方法来确定小流域不同地貌部位及不同侵蚀类型的产沙量。研究采用“粒度分折法”,对砒砂岩不同侵蚀类型区典型小流域泥沙来源进行了分析计算 ,结果表明 :砒砂岩区小流域泥沙主要来源于沟谷地 ,占小流域总产沙量的 79.39%～84 .89% ;沟间地产沙量占总产沙量的 15 .86 %～ 2 0 .6 1%。