向量场作图

1. 使用MATLAB 对微分方程组： 22

12x x y y xy ⎧=−−⎨=⎩&&

绘制向量场

x0=-2.8:.5:2.9;

y0=-2.8:.5:2.9;

[x y]=meshgrid(x0,y0);

d=sqrt((1-x.^2-y.^2).^2+(2*x.*y).^2); u=(1-x.^2-y.^2)./d;

v=(2*x.*y)./d;

hold on

quiver(x,y,u,v,0.3,'b');%绘画向量场

2. 使用MATLAB 画梯度图

22exp()z x x y =⋅−−，则梯度为 grad （z ）=,T

z z x y ⎡⎤∂∂⎢⎥∂∂⎣⎦ [x,y] = meshgrid(-2:.2:2,-1:.15:1); z = x .* exp(-x.^2 - y.^2);

[px,py] = gradient(z,.2,.15); contour(x,y,z), hold on

quiver(x,y,px,py), hold off, axis image