simpson1.cpp

这事辛普森积分算法实例

//Simpson method of Integration
//This is definite step version of c++

#include <iostream.h>
#include <math.h>
#include <iomanip.h>

int N;		//define the step:h=(b-a)/N

//-----------integrated fuction-------------
double f(double x)
{
	return exp(x)/(1+x*x);
}
//------------------------------------------

//-----------definite step version----------
double Simpson(double a,double b,double (*f)(double))
{
	double h=(b-a)/N;
	double simp=0.0;

	for(int i=1;i<=N;i++)
	{
		double x1=a+(i-1)*h;
		double midx=a+(i-0.5)*h;
		double x2=a+i*h;
		simp+= f(x1)+4*f(midx)+f(x2);
	}
	simp*=h/6;

	return simp;
}
//------------------------------------------

//-----------------main---------------------
void main()
{
	double x,y;
	
	cout<<"enter the lower limit,upper limit and step"<<endl;
	cin>>x>>y>>N;

	cout<<"The Integration(S method): "<<setprecision(9)<<Simpson(x,y,f)<<endl;
}
//------------------------------------------