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()
dx=0.1;
x=:dx:;
y=zeros(size(x));

x()=;
y()=;
for i=:length(x)-
%   z= y(i)+ (+y(i)) * dx;
%   y(i+)= y(i)+ ( (+y(i) + + z) /) * dx;
  y(i+)= y(i)+ (+y(i)) * dx;
end

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

logistic增长模型

%微分方程入下
%dp/dt=0.001*(-p)*p;
clc
clear
figure()
dx=0.1;
x=:dx:;
y=zeros(size(x));

x()=;
y()=;
for i=:length(x)-
%   z= y(i)+ (+y(i)) * dx;
%   y(i+)= y(i)+ ( (+y(i) + + z) /) * dx;
%   y(i+)= y(i)+ (+y(i)) * dx;
z=y(i) +0.001 *(-y(i))*y(i)*dx;
y(i+)=y(i) + ((0.001 *(-y(i))*y(i) + 0.001*(-z)*z )/  ) *dx;
end

plot(x,y)
grid on
hold on