微分方程:dy/dt=1+y; 解是y=2exp(x)-1;

clcclearfigure(2)dx=0.1;x=0:dx:8;y=zeros(size(x));x(1)=0;y(1)=1;for i=1:length(x)-1%   z= y(i)+ (1+y(i)) * dx;%   y(i+1)= y(i)+ ( (1+y(i) + 1+ z) /2) * dx;  y(i+1)= y(i)+ (1+y(i)) * dx;endplot(x,y)grid onhold onezplot('2*exp(x)-1',[0,8])

 logistic增长模型

%微分方程入下%dp/dt=0.001*(100-p)*p;clcclearfigure(2)dx=0.1;x=0:dx:100;y=zeros(size(x));x(1)=0;y(1)=10;for i=1:length(x)-1%   z= y(i)+ (1+y(i)) * dx;%   y(i+1)= y(i)+ ( (1+y(i) + 1+ z) /2) * dx;%   y(i+1)= y(i)+ (1+y(i)) * dx;z=y(i) +0.001 *(100-y(i))*y(i)*dx;y(i+1)=y(i) + ((0.001 *(100-y(i))*y(i) + 0.001*(100-z)*z )/2  ) *dx;endplot(x,y)grid onhold on