微分方程数值解Euler法

微分方程:dy/dt=1+y; 解是y=2exp(x)-1;

clc
clear
figure(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;
end

plot(x,y)
grid on
hold on
ezplot('2*exp(x)-1',[0,8])

 logistic增长模型

%微分方程入下
%dp/dt=0.001*(100-p)*p;
clc
clear
figure(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;
end

plot(x,y)
grid on
hold on