龙贝格公式计算定积分

 1 #include<stdio.h>    
 2 #include<math.h>
 3 #define maxlen 100
 4 #define eps 0.5*1e-5 
 5 double a=0;
 6 double b=1;
 7 double f(double x){
 8     return 4/(1+x*x);
 9 }
10 double t(int n){
11     int i;
12     double sum, h = (b - a) / n;
13     for (i = 1; i < n; i++)
14         sum += f(a + i * h);
15     sum += (f(a) + f(b)) / 2;
16     return (h * sum);
17 }
18 int main()
19 {
20     printf("k\t T[k]\t\t S[k]\t\t C[k]\t\t R[k]\n");
21     double T[maxlen];
22     double S[maxlen];
23     double C[maxlen];
24     double R[maxlen];
25     int k=-1;
26     while(1){
27         k++;
28         int z=pow(2,k);
29         T[k]=t(z);
30         if(k>0){
31             S[k]=T[k]*4/3-T[k-1]/3;
32         }
33         if(k>1){
34             C[k]=S[k]*16/15-S[k-1]/15;
35         }
36         if(k>2){
37             R[k]=C[k]*64/63-C[k-1]/63;
38         }
39         printf("%d\t %lf\t %lf\t %lf\t %lf\n",k+1,T[k],S[k],C[k],R[k]);
40         if(k>3){
41             if (abs(R[k]-R[k-1])<eps){
42                  break;
43             }
44         }
45     }    
46     printf("a:0,b:1 f(x):4/(1+x*x) eps:0.5*1e-5 the result:%lf\n",R[k]);
47     return 0;
48 }