c4.cpp

数值分析最常用的四十种算法

//C4.cpp
//Composite Simpson Rule

#include<iostream.h>

double f(double x)
{
	return 1/(1+x*x);
}

double ComSimp(double x0,double xn,int n)
{
	double s1,s2,h;
	int i;
	h=(xn-x0)/n;s1=f(x0+h/2);s2=0;        //Initialization
	for (i=1;i<n;i++)
	{
		s1+=f(x0+i*h+h/2);
		s2+=f(x0+i*h);
	}
    return h/6*(f(x0)+4*s1+2*s2+f(xn));
}

void main()
{
	double x0=0,xn=1;
	int n=100;
	cout<<ComSimp(x0,xn,n)<<endl;
}

//The answer:0.785398，
//与精度达e-15的精确值0.78539816339745已经相当接近
//算法耗时短,Simpson的确是一种相当理想的的求积方法