simpson.cpp

用复化Simpson积分公式计算积分的通用程序

#include<iostream>
#include<math.h>
#include<iomanip>
using namespace std;

//#define f(x) sin(x)
//#define I(x) cos(x)

#define f(x) log(x)
#define I(x) 1/x

double simpson(double up,double down,int n)
{
	int i,m = n/2;
	double h = (up - down)/n;
	double S,temp1,temp2;
	temp1 = temp2 = 0;

	for(i=0;i<=m-1;i++)
	{
		temp1 += f(down+(2*i+1)*h);
	}
	for(i=1;i<=m-1;i++)
	{
		temp2 += f(down+2*i*h);
	}

	S = h * ( f(down) + 4*temp1 + 2*temp2 +f(up) )/3;
	return S;
}

double error(double up,double down,double S)
{
	double P = I(down) - I(up);
	return P - S;
}

int main()
{
	double up,down;
	cout<<"Please input the up boundary and the down boundary:"<<endl;
	cin>>up;
	cin>>down;

	cout.precision(18);
	cout.setf(ios::fixed);

	for(int k=0;k<=12;k++)
	{
		int n = pow(2,k);
		double S = simpson(up,down,n);
		cout<<"When k = "<<k<<":"<<endl;
		cout<<"复化Simpson积分可得结果为: "<<S<<endl;
		cout<<"  ***********  AND 误差为: "<<error(up,down,S)<<endl;
	}
	return 0;
}