for_ordinary_differential_equation.cpp

用用改进欧拉法解常微分方程的问题,并应用该算法于实际问题.并在程序结果路比较用表列出近似解yi

#include <iostream.h>
//定义函数表达式，其中函数表达式包含两个变量x和y,并反回函数表达式f的值.
double fxy(double x, double y)
{ double f;
  f=-x*y*y;
  return f;
}
//求函数表达式f的导数，并反回其的值。
double f(double x)
{ double y;
  y=2/(1+x*x);
  return y;
}
  
void main()
{  int n;
   double x0,xn,y0;//给定初始值
   double h,x,y;
   double yp,yc;
   cout<<"please input x0:"<<endl;
   cin>>x0;
   cout<<"please input y0:"<<endl;
   cin>>y0;
   cout<<"please input xn:"<<endl;
   cin>>xn;
   cout<<"please input n:"<<endl;
   cin>>n;
   h=(xn-x0)/n;
   cout<<"output the h="<<h<<endl;
   y=y0;
   x=x0;
   cout<<"xi"<<'\t'<<"yi"<<'\t'<<'\t'<<"y(i)"<<endl;
   cout<<"*******************************"<<endl;
   while(x<=xn)
   {cout<<x<<'\t'<<y<<'\t'<<'\t'<<f(x)<<endl;
    yp=y+h*fxy(x,y);
	x=x+h;
	yc=y+h*fxy(x,yp);
	y=0.5*(yp+yc);
   }
}