一类常微分方程初值问题的精度和误差分析  

The precision and error analysis of the initial value problems of a class of ordinary differential equations

作　　者：耿红梅[1] 

机构地区：[1]扬州工业职业技术学院基础部,江苏扬州225127

出　　处：《高师理科学刊》2012年第6期11-13,共3页Journal of Science of Teachers＇College and University

摘　　要：对问题P_2{u′(t)=f(t,u(t))0<t≤t u′(0)=u_0(其中:f(t,u)是具有期望的、有界的高阶连续偏导数)给出一个二阶精度的计算格式,并证明其收敛性.对f(t,u)=4tu/(1+t^2)+1,u_0=0,用所给格式和经典的四阶Runge-Kutta法计算u(t)在t∈[0,2]内的近似值,精确到0.0001,并与解析解u=1/(1+t^2)(1/5t^5+2/3t^3+t进行比较.Gave a two order accuracy format to the problem P3：{u（0）=u0u＇（t）=f（t,u（t））0〈t〈^Tand proved its astringency. In which f（t, u） is expected and bounded continuous high order partial derivative. To the f（t,u）=-1＋t^2-^4tu＋1,u0=0,andu（t）aceurates to 0.000 1. Then the approximate of u（t） was compared with the analytical solutions of u=（1＋t^2）^-1（5-1t5＋3-2t^3＋t）.

关 键 词：常微分方程 初值问题 改进Euler法 四阶Runge—Kutta法 

分 类 号：O241.81[理学—计算数学]