改进的欧拉公式.cpp

分段算法的程序

//以y'=y-2*x/y 为例其中0<=x<=1,y(0)=1
#include<iostream.h>
#include<math.h>
#include<iomanip.h>

double f(double x);

double f(double x,double y)
{
	double w;
	w=y-2.0*x/y;
	return w;
}

void main(void)
{
	double x,y,y1,h,p,yp,yc;
	int i,n;
	cout<<"请输入x,y和h的值："<<endl;
	cout<<"x=";
	cin>>x;
	cout<<"y=";
	cin>>y;
	cout<<"h=";
	cin>>h;
	n=(y-x)/h;
	cout<<"n="<<n<<endl;
	for(i=1;i<=n;i++)
	{	
		yp=y+h*f(x,y);
		yc=y+h*f(x+h,yp);
		p=(yp+yc)/2.0;
		x=x+h;
		y=p;
		y1=sqrt(1+2.0*x);
		cout<<"x="<<x<<setw(8)<<"y="<<setprecision(6)<<p<<setw(8)<<"y*="<<setprecision(6)<<y1<<endl;
	}
}