自动选取步长simpson公式求积分算法.cpp

数值分析课程必备的算法：自动选取步长Simpson公式求积分算法。有需要的同学下载

//自动选取步长Simpson公式求积分算法
	
#include<iostream.h>
#include<math.h>

double fun(double);
void main()
{	
	double a,b,h,e,S1,S2,T0,T1;
	int n;
	
	cout<<"**************自动选取步长Simpson公式求积分算法**************"<<endl;
	cout<<"请输入积分区间的[a,b]:"<<endl;
	cout<<"a= ";		cin>>a;
	cout<<"b= ";		cin>>b;

	cout<<"请输入容许误差e:"<<endl;
	cout<<"e= ";		cin>>e;

	h=(b-a)/2;
	T1=((b-a)/6*(fun(a)+4*fun((a+b)/2)+fun(b)));
	n=1;
	

	int flag=1;
	while(flag==1)
	{	
		T0=T1;		S1=0;		S2=0;

		for (int k=1;k<=n;k++)
		{
			S1+=fun(a+(2*k-1)*(b-a)/(2*n));
		}
		for ( k=1;k<=n-1;k+=2)
		{
			S2+=fun(a+k*(b-a)/n);
		}

		T1=T0/2+2*(b-a)*S1/n/3-(b-a)*S2/(3*n);
		

		if (fabs(T1-T0)<15*e) 
		{	flag=0;
			cout<<"所求函数f(t)=2/(1+t*t)在["<<a<<","<<b<<"]的积分近似值为:"<<T1<<endl;
		}
		else {	n=2*n;	flag=1;	}	
	}
}
double fun(double x)
{	return 2/(1+x*x);	}