微分方程数值解 Adams.doc

宋玉霞 2008050216 统数 信科0802 实验一_2:Adams方法一、 实验题目：取步长二、 实验要求：用Adams公式，求此微分方程在0，10上的数值解，并与精确解进行比较。三、 程序运行结果结果：y = Columns 1 through 11 0 0.0100 0.0400 0.0900 0.1600 0.2500 0.3600 0.4900 0.6400 0.8100 1.0000 Columns 12 through 22 1.2100 1.4400 1.6900 1.9600 2.2500 2.5600 2.8900 3.2400 3.6100 4.0000 4.4100 Columns 23 through 33 4.8400 5.2900 5.7600 6.2500 6.7600 7.2900 7.8400 8.4100 9.0000 9.6100 10.2400 Columns 34 through 44 10.8900 11.5600 12.2500 12.9600 13.6900 14.4400 15.2100 16.0000 16.8100 17.6400 18.4900 Columns 45 through 55 19.3600 20.2500 21.1600 22.0900 23.0400 24.0100 25.0000 26.0100 27.0400 28.0900 29.1600 Columns 56 through 66 30.2500 31.3600 32.4900 33.6400 34.8100 36.0000 37.2100 38.4400 39.6900 40.9600 42.2500 Columns 67 through 77 43.5600 44.8900 46.2400 47.6100 49.0000 50.4100 51.8400 53.2900 54.7600 56.2500 57.7600 Columns 78 through 88 59.2900 60.8400 62.4100 64.0000 65.6100 67.2400 68.8900 70.5600 72.2500 73.9600 75.6900 Columns 89 through 99 77.4400 79.2100 81.0000 82.8100 84.6400 86.4900 88.3600 90.2500 92.1600 94.0900 96.0400 Columns 100 through 101 98.0100 100.0000yy = Columns 1 through 11 0 0 0.0400 0.0900 0.1600 0.2500 0.3600 0.4900 0.6400 0.8100 1.0000 Columns 12 through 22 1.2100 1.4400 1.6900 1.9600 2.2500 2.5600 2.8900 3.2400 3.6100 4.0000 4.4100 Columns 23 through 33 4.8400 5.2900 5.7600 6.2500 6.7600 7.2900 7.8400 8.4100 9.0000 9.6100 10.2400 Columns 34 through 44 10.8900 11.5600 12.2500 12.9600 13.6900 14.4400 15.2100 16.0000 16.8100 17.6400 18.4900mns 45 through 55 19.3600 20.2500 21.1600 22.0900 23.0400 24.0100 25.0000 26.0100 27.0400 28.0900 29.1600 Columns 56 through 66 30.2500 31.3600 32.4900 33.6400 34.8100 36.0000 37.2100 38.4400 39.6900 40.9600 42.2500 Columns 67 through 77 43.5600 44.8900 46.2400 47.6100 49.0000 50.4100 51.8400 53.2900 54.7600 56.2500 57.7600 Columns 78 through 88 59.2900 60.8400 62.4100 64.0000 65.6100 67.2400 68.8900 70.5600 72.2500 73.9600 75.6900 Columns 89 through 99 77.4400 79.2100 81.0000 82.8100 84.6400 86.4900 88.3600 90.2500 92.1600 94.0900 96.0400 Columns 100 through 101 98.0100 100.0000ee = 1.0e-012 * Columns 1 through 11 0 0 0 0 0 -0.0001 -0.0001 -0.0002 -0.0002 -0.0003 -0.0004 Columns 12 through 22 -0.0004 -0.0002 0 0.0002 0.0009 0.0009 0.0013 0.0013 0.0018 0.0018 0.0018 Columns 23 through 33 0.0027 0.0036 0.0044 0.0044 0.0053 0.0053 0.0062 0.0071 0.0089 0.0089 0.0089 Columns 34 through 44 0.0107 0.0107 0.0124 0.0124 0.0124 0.0142 0.0160 0.0142 0.0142 0.0071 0.0036 Columns 45 through 55 0 -0.0036 -0.0071 -0.0107 -0.0142 -0.0142 -0.0178 -0.0213 -0.0249 -0.0284 -0.0355 Columns 56 through 66 -0.0391 -0.0426 -0.0497 -0.0568 -0.0639 -0.0639 -0.0711 -0.0711 -0.0782 -0.0782 -0.0853 Columns 67 through 77 -0.0853 -0.0924 -0.0995 -0.0995 -0.1066 -0.1137 -0.1208 -0.1208 -0.1279 -0.1279 -0.1350 Columns 78 through 88 -0.1492 -0.1492 -0.1563 -0.1634 -0.1705 -0.1705 -0.1705 -0.1847 -0.1847 -0.1847 -0.1990 Columns 89 through 99 -0.2132 -0.2132 -0.2132 -0.2274 -0.2416 -0.2416 -0.2416 -0.2558 -0.2558 -0.2558 -0.2700 Columns 100 through 101 -0.2842 -0.2842四、程序附录：1. function f=fun2(x,y)%右端函数f=2*x;2. function x,y,yy,ee =adams2(x0,y0,xfinal,h)%用Adams求解n=(xfinal-x0)/h; hh=h/2;x(1)=x0;y(1)=y0;x(2)=x0+h;y(2)=0.01;%for i=2:n y(i+1)=y(i