% IntegByEulerpro.m
%
%   Author: HUANG Huajiang
%   Copyright 2003 UNILAB Research Center, 
%   East China University of Science and Technology, Shanghai, PRC
%   $Revision: 1.0 $  $Date: 2003/05/21 $

clear all
clc

x0 = 0;     % 積分下限
xf = 1;     % 積分上限
y0 = 1;     % 初始值
h = 0.1;    % 積分步長

n = fix((xf-x0)/h);
x(1) = x0;
y(1) = y0;

for i = 1:n-1
    x(i+1) = x0 + i*h;
    y1 = y(i) + h*(-y(i)+x(i)+1);
    y2 = y(i) + h*(-y1+x(i+1)+1);
    y(i+1) = (y1 + y2)/2;
end
plot(x,y)