新建 文本文档 (2).txt

数值分析中的龙贝格积分的C语言实现源程序

#include <iostream>
#include <cmath>
#include <iomanip>
using namespace std;
double fun1(double x)     /*计算f(x)的值*/ 
{
	if (x==0)
	return 1;
	else 
		return (sin(x)/x);
}
double fun2(double x,double h)      /*累计求和s*/
{
	double s=0.00;
	while (x<1)
	{
		s+=fun1(x);
		x+=h;
	}
	return s;
}
void main()
{
	int t,a=0,b=1,k=0;
	double t1,t2,s1,s2,c1,c2,r1,r2,h;
	h=b-a;
	t1=(fun1(a)+fun1(b))*h/2;
	cout<<"计算的数据如下:"<<endl;
	cout<<setw(9)<<"K"<<setw(13)<<"S"<<setw(14)<<"C"<<setw(12)<<"R"<<endl<<endl;
	cout<<k<<setw(13)<<setprecision(8)<<t1<<endl;
	for (k=1;k<=5;k++)
	{
		if (k==1)
		{
			t=pow(2,1);
			t2=t1/2+fun2(a+h/t,2*h/t)*h/t;
			s2=4*t2/3-t1/3;
			cout<<k<<setw(13)<<setprecision(8)<<t2<<setw(13)<<setprecision(8)<<s2<<endl;
		}
		if (k==2)
		{
			t=pow(2,2);
			t1=t2;s1=s2;
			t2=t1/2+fun2(a+h/t,2*h/t)*h/t;
			s2=4*t2/3-t1/3;
			c2=16*s2/15-s1/15;
			cout<<k<<setw(13)<<setprecision(8)<<t2<<setw(13)<<setprecision(8)<<s2<<setw(13)<<setprecision(8)<<c2<<endl;
		}
		if (k==3)
		{
			t=pow(2,3);
			t1=t2;s1=s2;c1=c2;
			t2=t1/2+fun2(a+h/t,2*h/t)*h/t;
			s2=4*t2/3-t1/3;
			c2=16*s2/15-s1/15;
			r2=64*c2/63-c1/63;
			cout<<k<<setw(13)<<setprecision(8)<<t2<<setw(13)<<setprecision(8)<<s2
				<<setw(13)<<setprecision(8)<<c2<<setw(13)<<setprecision(8)<<r2<<endl;
		}
		if (k==4)
		{
			t=pow(2,4);
			t1=t2;s1=s2;c1=c2;r1=r2;
			t2=t1/2+fun2(a+h/t,2*h/t)*h/t;
			s2=4*t2/3-t1/3;
			c2=16*s2/15-s1/15;
			r2=64*c2/63-c1/63;
			cout<<k<<setw(13)<<setprecision(8)<<t2<<setw(13)<<setprecision(8)<<s2
				<<setw(13)<<setprecision(8)<<c2<<setw(13)<<setprecision(8)<<r2<<endl;
			if ((r2-r1)<1/2*1e-7)						
				cout<<"积分值为："<<r1<<endl;
		}
		if ((k==5)&&((r2-r1)>1e-7))
		{
			t=pow(2,5);
			t1=t2;s1=s2;c1=c2;r1=r2;
			t2=t1/2+fun2(a+h/t,2*h/t)*h/t;
			s2=4*t2/3-t1/3;
			c2=16*s2/15-s1/15;
			r2=64*c2/63-c1/63;
			cout<<k<<setw(13)<<setprecision(8)<<t2<<setw(13)<<setprecision(8)<<s2
			<<setw(13)<<setprecision(8)<<c2<<setw(13)<<setprecision(8)<<r2<<endl;
			if ((r2-r1)<1/2*1e-7)
		    	cout<<"积分值为："<<r2<<endl;
		}
	}
}