-190.7388 16.4525 118.6963 123.0361 33.0336 -57.2817 37.3849 -66.8175 160.6261 69.9436 65.2278 -21.4319 170.2597 92.8549 -75.5045 -138.7923 -52.6574 -8.4902 115.9030 -189.3844 34.0593 -109.1584 20.6169 136.7896 -45.4089 135.7386 -10.7050 10.4240 Gi =
199.1404 33.1590 -86.1452 -7.5887 -181.6856 -145.4039 18.9686 16.5731 11.9053 -4.5021 87.0651 148.4022 127.5072 -7.2483 25.1791 -84.0887 -233.6194 135.0018 -128.3931 -28.4923 53.7385 41.5139 -24.4788 120.7113 0.8532 66.7238 -160.2738 -55.1871
28.6287 -75.6522 128.8596 -133.7671 3.1772 -282.0866 -13.7111 158.5203 -24.2673 -189.7767 -83.3384 16.7992 21.0869 67.0898 -182.1134 -180.7631 -143.6344 20.6149 80.5622 87.7339 9.4764 228.1237 Gn =
1.0253e+03
第四章 1 数值差分
d=0.001;
dxdt_diff=diff(y)/d;
dxdt_grad=gradient(y)/d; hold on;
plot(t,y,'-r');
plot(t(1:end-1),dxdt_diff,'-g'); plot(t,dxdt_grad,'-b');
210-1-2-3-4-5-601234567数值求导后存在很多的毛刺
2 数值计算
d=1e-5; t=0:d:10;
t=t+(t==0)*realmin;%去除影响 fx=sin(t)./t;
y=cumtrapz(fx)*d; plot(t,y);
yt1=find(t==4.5); y45=y(yt1)
y45 =
1.6541
21.81.61.41.210.80.60.40.20012345678910尝试integral d=1e-5; t=0:d:10;
t=t+(t==0)*realmin;%去除影响 fx=@(t)sin(t)./t; y=integral(fx,0,10) %plot(t,y);
%yt1=find(t==4.5); %y45=y(yt1)
y =
1.6583
3 数值积分
d=1e-5; t=0:d:pi;
t=t+(t==0)*realmin;%去除影响 fx=@(t)exp((sin(t)).^3); s=integral(fx,0,pi)
s =
5.1370
符号验算
syms x;
fxx=exp((sin(x))^3); ss=int(fxx,x,0,pi)
ss =
int(exp(sin(x)^3), x, 0, pi)
此时符号运算不如数值运算可以得出解析解
4 求数值积分
clear;
fx=@(x)exp(-abs(x)).*abs(sin(x)); format long ;
s=integral(fx,-5*pi,inf,'Abstol',1e-9)
s =
1.090331100328886
x=linspace(-5*pi,50,1e7); dx=x(2)-x(1);
st=trapz(exp(-abs(x)).*abs(sin(x)))*dx
st =
1.090331328559288
可知，trapz必须为有限数值；同样，quadl也需为有限数值
clear;
fx=@(x)exp(-abs(x)).*abs(sin(x)); format long ;
s=quadl(fx,-5*pi,50,1e-9)
s =
1.090331336243919
5 最小值点
%首先绘出函数曲线，确定大概找最小值范围 clear;
ft=@(t)sin(5*t).^2.*exp(0.06*t.*t)+1.8*abs(t+0.5)-1.5*t.*cos(2*t); t=-5:0.01:5;
ezplot(ft,[-5,5]); sin(5 t)2 exp(0.06 t t)+...-1.5 t cos(2 t)20181614121086420-5-4-3-2-10t12345