function [x,y] = eulerpro(fun,x0,xf,y0,h)
% 功能：用改進的歐拉方法計算一階常微分方程的初值問題
% fun: 微分方程的f(x,y)函數句柄或函數名
% x0: 積分下限
% xf: 積分上限
% h: % 積分步長
%
%   Author: HUANG Huajiang
%   Copyright 2003 UNILAB Research Center, 
%   East China University of Science and Technology, Shanghai, PRC
%   $Revision: 1.0 $  $Date: 2003/05/21 $

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*feval(fun,x(i),y(i));
    y2 = y(i) + h*feval(fun,x(i+1),y1);
    y(i+1) = (y1 + y2)/2;
end