【C/C++】实现龙贝格算法

 1 #include<stdio.h>
 2 #include<math.h>
 3 #include<iostream>
 4 #include<cstdio>
 5 using namespace std; 
 6 int Rk=0;
 7 int Tk=0;
 8 double fx(double x)   //被积函数
 9 {
10     //if(x==0.0)return 1.0;
11     return 3*x*x*x+2*x*x+1 + sin(x);
12 }
13 double getReal(double a,double b){
14     double r1 = 3.0/4.0 * b*b*b*b + 2.0/3.0*b*b*b + b - cos(b);
15     double r2 = 3.0/4.0 * a*a*a*a + 2.0/3.0*a*a*a + a - cos(a);
16     return r1 - r2;
17 }
18 double getS(double a,double b,double h)
19 {
20     double res=0.0;
21     for(double i=a+h/2.0; i<b; i+=h){
22         res+=fx(i);    
23     }
24         
25     return res;
26 }
27 double Romberg(double a,double b,double e)
28 {
29     int k=1;
30     double T1,T2,S1,S2,C1,C2,R1,R2;
31     double h=b-a;
32     double s;
33     T1=(fx(a)+fx(b))*h/2.0;
34     int counter=0;
35     while(1)
36     {
37         Rk++;
38         counter++;
39         s=getS(a,b,h);
40         T2=(T1+h*s)/2.0;
41         S2=(4.0*T2-T1)/3.0;
42         h/=2.0;
43         T1=T2;
44         S1=S2;
45         C1=C2;
46         R1=R2;
47         if(k==1)
48         {
49             k++;
50             continue;
51         }
52         C2=(16.0*S2-S1)/15.0;
53         if(k==2)
54         {
55             k++;
56             continue;
57         }
58         R2=(64.0*C2-C1)/63.0;
59         if(k==3)
60         {
61             k++;
62             continue;
63         }
64         if(fabs(R1-R2)<e||counter>=100)break;
65     }
66     return R2;
67 }
68 double Tn(double a,double b,double e)
69 {
70     double T1,T2;
71     double h=b-a;
72     T1=(fx(a)+fx(b))*h/2.0;
73     while(1)
74     {
75         Tk++;
76         double s=getS(a,b,h);
77         T2=(T1+h*s)/2.0;
78         if(fabs(T2-T1)<e)break;
79         h/=2.0;
80         T1=T2;
81     }
82     return T2;
83 }
84 int main()
85 {
86     double a,b,e;
87     printf("输入积分限和精度： a b e:");
88     //输入区间[a,b],和精度e
89     scanf("%lf%lf%lf",&a,&b,&e);
90     double t=Romberg(a,b,e);
91     //分别输出龙贝格算法和梯形法的计算结果和相应二分次数
92     printf("\nRomberg:积分值：%.7lf  --  二分次数：%d\n",t,Rk);
93     t=Tn(a,b,e);
94     printf("     Tn:积分值：%.7lf  --  二分次数：%d\n",t,Tk);
95     double tf = getReal(a,b);
96     printf("    Real:%.7lf",tf);
97     return 0;
98 }