Question

Matlab中数值计算的相关题目，求大神帮帮忙解决！

Answer 1

1.y0 = @(t) sin(t)./t;
x = 0:0.01:10;
y = zeros(size(x));
for i = 2:size(x,2)
y(i) = quad(y0,0,x(i));
end
plot(x,y,'k-');

追答

2.
y0 = @(x) exp(-abs(x)).*sin(abs(x));
y = quad(y0,-5*pi,1.7*pi,1e-9)

y =

1.0005

3
t = -5:0.001:5;
f = sin(5*t).^2.*exp(0.06*t.*t)-1.5*t.*cos(2*t)+1.8*abs(t+0.5);
min = min(f)

min =

-0.1860

4
A = magic(4);
b = [1;2;3;4];
x = A\b

警告: 矩阵接近奇异值，或者缩放错误。结果可能不准确。RCOND = 1.306145e-17。
> In test at 6

x =

1.0e+15 *

-0.5629
-1.6888
1.6888
0.5629

这个结果是不正确的。正确的计算方法我还要再想想

第5题是要求t为多少时的y？图片上没照出来

6.
[x,y] = solve('sin(x-y) = 0','cos(x+y) = 0')

x =

(3*pi)/4
-(3*pi)/4
pi/4
-pi/4

y =

-pi/4
pi/4
-(3*pi)/4
(3*pi)/4

追问

十分感谢您！

5题是t＝0.5时

追答

补充第5题

y1 = dsolve('D2y-3*Dy+2*y = 1','y(0) = 1','Dy(0) = 0','t');
tspan = [0 1];
[t,y2] = ode45(@myodefun,tspan,[1 0]);

y3 = double(subs(y1,'t',0.5));
pos = 0;
for i = 1:size(t,1)-1
if t(i+1) >= 0.5
pos = i;
break;
end
end
k = (0.5-t(pos))/(t(pos+1)-t(pos));
y4 = y2(pos,1)+k*(y2(pos+1,1)-y2(pos,1));
disp(['t = 0.5时数值解为： ' num2str(y4) ' 符号解为： ' num2str(y3)]);
hold on;
y5 = double(subs(y1,'t',t));
plot(t,y2(:,1),'r*',t,y5,'k-');
legend('数值解','符号解');

下面是自定义的子函数

function dy = myodefun(t,x)
dy = zeros(2,1);
dy(1) = x(2);
dy(2) = 3*x(2)-2*x(1)+1;
end