实例89　辛普生数值积分

#include <stdio.h>
#include <math.h>
 
double Function(double);
double SIMP1(double,double,int);
double SIMP2(double,double,double);
 
void main()
{
    double a1,b1,eps;
    int n1;
    double Result1;
    double Result2;
    a1 = 0.0;
    b1 = 0.8;
    n1 = 4;
    eps = 5e-7;
    Result1 = SIMP1(a1,b1,n1);
    Result2 = SIMP2(a1,b1,eps);
    printf("利用定步长辛普生积分结果为：\n");
    printf("I1 = %.10f\n",Result1);
    printf("利用变步长辛普生积分结果为：\n");
    printf("I2 = %e\n",Result2);
}
 
double SIMP1(a,b,n)
double a;
double b;
int n;
{
    int i;
    double h,s;
    h=(a-b)/(2*n);
    s=0.5*(Function(a)-Function(b));
    for(i=1;i<=n;i++)
        s+=2*Function(a+(2*i-1)*h)+Function(a+2*i*h);
    return((b-a)*s/(3*n));
}
 
double SIMP2(a,b,eps)
double a;
double b;
double eps;
{
    int k,n;
    double h,t1,t2,s1,s2,p,x;
    n=1;
    h=b-a;
    t1=h*(Function(a)+Function(b))/2;
    s1 = t1;
    while(1)
    {
        p = 0;
        for(k=0;k<=n;k++)
        {
            x = a+(k+0.5)*h;
            p+=Function(x);
        }
        t2=(t1+h*p)/2;
        s2=(4*t2-t1)/3;
        if(fabs(s2-s1)>=eps)
        {
            t1=t2;
            n=n+n;
            h=h/2;
            s1=s2;
            continue;
        }
        break;
    }
    return(s2);
}
 
double Function(double x)
{
    return(cos(x));
}

trust100@ubuntu:~/test/clanguage$ ./a.out 
利用定步长辛普生积分结果为：
I1 = 0.7173564899
利用变步长辛普生积分结果为：
I2 = 7.173566e-01