跳绳曲线的数值解及误差估计的间接判定法

来源期刊：中南大学学报(自然科学版)1995年第4期

论文作者：何竞飞

文章页码：532 - 535

关键词：数值分析; 误差估计; 跳绳曲线

Key words：numerical analysis; error evaluation; rope skipping curve

摘    要：跳绳曲线的微分方程是不可积方程,而且其边界斜率的倒数为无穷大。因此,必须用中插法求其坐标的数值解;此外,用直接数值分析的方法,不能得到准确的误差估计值。作者用曲线与坐标轴所围面积的数值解与其实际值的误差,来间接判定曲线坐标数值解的误差估计值,准确度高.

Abstract: The differential equation of the rope skipping curve is an unintegratle fuction,and thesIope on the curve's boundary is equal to infinity.For this reason,it is necessary to use themiddle insert for calculating the numerical solution of the curve,and it is impossible to usethe direct numerical analysis for evaluating accuratly its error.The paper suggests using theerror between the numerical solution of the area among the curve and coordinate axes and itsreality solution for evaluating the error of the numerical solution of the curvem,which hashigh degree of accuracy.