积分的近似求法.cpp

C++Example实用的算法:包括枚举

//利用辛普森变步长公式求积分
#include<iostream.h>
#include<iomanip.h>
#include<math.h>

//被积函数的定义
double fun(double x)
{
	return exp(x)/(1+x*x);
}

//计算精度
const double eps=1e-4;

void main()
{
	int n=1;
    double start=0;
	double end=1;
	double height=end-start;
   	double I2n=height*(fun(start)+fun(end));
	double T2n=I2n;
	double Tn,In=0;
	
	while(fabs(I2n-In)>=eps)
	{
		Tn=T2n;
		In=I2n;
		double sigma=0;
		for(int k=0;k<n;k++)
		{
			sigma=sigma+(start+(k+0.5)*height);
		}
		
		T2n=(Tn+height*sigma)/2.0;
        In=(4*T2n-Tn)/3.0;
		
		n=n*2;
		height=height/2;
	}
    cout<<"The integral of fun() from "<<start<<" to "
		<<end<<" is : "<<endl;
	cout<<setiosflags(ios::fixed)
		<<setprecision(10)
		<<setw(12)
		<<T2n
		<<endl;
}