关于常微分方程初值问题数值解误差的探讨  

Some discussion for numerical solution of initial value problem of an ordinary differential equation

作　　者：徐应祥[1] 

机构地区：[1]西北师范大学数学与信息科学学院,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2003年第1期19-23,共5页Journal of Northwest Normal University(Natural Science)

摘　　要：引用B样条插值函数讨论了一阶常微分方程初值问题的数值解 ,给出一个隐式近似求解公式 ,并得到此公式的局部截断误差为O(h5) ,整体截断误差为O(h4 ) .在此基础上又给出了一个校正显式求解公式 ,其局部截断误差为O(h4 ) .By use of interpolating B spline function,the numerical solution of initial value problem of an ordinary differential equation is discussed.An inexplicit approximate solving formula is given,from which implies its local truncation error is O(h 5),but the global truncation error is O(h 4).On this bases,an explicit revise formula for the problem is obtained,and its local truncation error is O(h 4).

关 键 词：常微分方程 局部截断误差 整体截断误差 B样条插值函数 初值问题 数值解 

分 类 号：O175.1[理学—数学] O241.81[理学—基础数学]