2012年下学期数学实验作业参考

1.0000 -0.0001 1.0000 -0.0003 1.0000 -0.0004 1.0000 -0.0007 1.0000 -0.0010 0.9999 -0.0015 0.9999 -0.0022 0.9998 -0.0031 0.9997 -0.0044 0.9996 -0.0064 0.9993 -0.0092 0.9988 -0.0132 0.9981 -0.0191 0.9968 -0.0277 0.9947 -0.0405 0.9908 -0.0597 0.9837 -0.0896 0.9683 -0.1414 0.9398 -0.2147 0.8990 -0.2928 0.8503 -0.3618 0.7924 -0.4213 0.7249 -0.4684 0.6492 -0.4994 0.5680 -0.5110 0.4862 -0.5015 0.4084 -0.4711 0.3384 -0.4210 0.2791 -0.3527 0.2321 -0.2671 0.1989 -0.1628 0.1823 -0.0343 0.1833 0.0525 0.1936 0.1394 0.2125 0.2209 0.2417 0.2995 0.2811 0.3678 0.3302 0.4181 0.3881 0.4421 0.4495 0.4316

0.4696 0.4202

49

2.6洛伦兹(Lorenz)方程组是由三个一阶微分方程组成的方程组.这三个方程看似简单, 也没有包含复杂的函数, 但它的解却很有趣和耐人寻味. 试求解洛伦兹方程组

?x?(t)?16y(t)?16x(t)???y(t)??x(t)z(t)?45x(t)?y(t), ??z(t)?x(t)y(t)?4z(t)???x(0)?12,y(0)?4,z(0)?0并画出解曲线的图形.

function dy=lorenz(t,y)

dy=zeros(3,1);dy(1)=16*y(2)-16*y(1);

dy(2)=-y(1)*y(3)+45*y(1)-y(2);dy(3)=y(1)*y(2)-4*y(3);

[T,Y]=ode45('lorenz',[0 0.1],[12 4 0]) plot(T,Y(:,1),'-',T,Y(:,2),'*',T,Y(:,3),'+') T =

0 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0003 0.0004 0.0005 0.0007 0.0013 0.0020 0.0026

50

0.0033 0.0058 0.0083 0.0108 0.0133 0.0158 0.0183 0.0208 0.0233 0.0258 0.0283 0.0308 0.0333 0.0358 0.0383 0.0408 0.0433 0.0458 0.0483 0.0508 0.0533 0.0558 0.0583 0.0608 0.0633 0.0658 0.0683 0.0708 0.0733 0.0758 0.0783 0.0808 0.0833 0.0858 0.0883 0.0908 0.0933 0.0950 0.0966 0.0983 0.1000 Y =

12.0000 11.9999 11.9997 11.9996 11.9995 11.9988 11.9981 11.9975 11.9968 11.9934

4.0000 0 4.0006 0.0001 4.0011 0.0001 4.0017 0.0002 4.0022 0.0002 4.0050 0.0005 4.0079 0.0007 4.0107 0.0010 4.0135 0.0012 4.0275 0.0025 51

11.9901 4.0415 0.0037 11.9868 4.0555 0.0050 11.9835 4.0695 0.0063 11.9670 4.1395 0.0127 11.9507 4.2093 0.0192 11.9346 4.2790 0.0258 11.9187 4.3486 0.0326 11.8416 4.6950 0.0676 11.7690 5.0386 0.1049 11.7007 5.3797 0.1446 11.6367 5.7182 0.1865 11.4298 6.9914 0.3669 11.2804 8.2360 11.1853 9.4575 11.1413 10.6612 11.1460 11.8517 11.1970 13.0336 11.2923 14.2107 11.4299 15.3865 11.6083 16.5644 11.8260 17.7471 12.0816 18.9369 12.3740 20.1357 12.7022 21.3451 13.0651 22.5660 13.4620 23.7988 13.8918 25.0437 14.3538 26.2998 14.8472 27.5659 15.3710 28.8399 15.9244 30.1193 16.5063 31.4003 17.1155 32.6786 17.7509 33.9488 18.4108 35.2047 19.0938 36.4388 19.7977 37.6428 20.5206 38.8071 21.2598 39.9212 22.0125 40.9734 22.7755 41.9510 23.5453 42.8405 24.3177 43.6275 25.0885 44.2970 25.8527 44.8337 26.6052 45.2222 27.3402 45.4476 27.8220 45.5001 28.2913 45.4679 28.7462 45.3473 29.1845 45.1348

0.5783 0.8197 1.0908 1.3920 1.7238 2.0877 2.4850 2.9180 3.3890 3.9006 4.4560 5.0584 5.7117 6.4197 7.1867 8.0170 8.9154 9.8867 10.9358 12.0678 13.2876 14.6002 16.0103 17.5221 19.1398 20.8666 22.7049 24.6563 26.7213 28.8986 31.1856 33.5776 36.0682 38.6483 41.3068 43.1334 44.9845 46.8548 48.7385 52