Integral calculus using analytically and Simpson methods

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December 6th, 2012, 05:56 AM

frenchcookie

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Integral calculus using analytically and Simpson methods

Hello,
I have problem with my program. I am trying to calculate analytically the value of integral with two different set of parameters

URL

and then for both I calculate the value using Simpson rule.

I don't know how to modify my code to calculate a) with Simpson rule, because now all the results are the same n and I don't know why after n=15 all my results are 0.

I was reading about double representation and I was analysing the Simpson rule and my analytically code for integral but I can't figure it out why there are 0, because I calculate it with Mathematica to improve my results and it gives
my some numbers not 0.

For now I have this code, the results from section b) and analytically from a) are ok expect n>15 where I have 0.

Code:

 
    #include <iomanip>
    #include <iostream>
    #include <cmath>
    #include <fstream>
     
    using namespace std;
    const int N = 1;
     
    double f(double x)
    {
        double dx, b=2.0, z, p;
        int n;
        for(n=1;n<=20;n++){
            p=1 - (pow(10.0, (-n)));
            z=1/(pow(x, p));
        return z;}
    }
     
    double fx(double x)
    {
        double n;
        double p=0.5;
        double b=1 + (pow(10.0, (-n)));
        double dx=(b-1)/N;
        double z=dx/(pow(x, p));
        return z;
    }
     
    int main()
    {
       
        ofstream PLIK;
       
       
        double a, b, s1,s2,s3,s4,x, p; int i;
        int n;
        s1=0;s3=0;
        s2=0;s4=0;
       
        cout.unsetf(ios::floatfield);            
        cout.precision(16);
       PLIK.open("RESULTS.txt");
       
     
        cout << "ANALYTICALLY." << endl;
        PLIK<<"ANALYTICALLY A<<endl;
       cout << "SECTION A:" << endl; // Podpunkt pierwszy
       for (n = 1; n <= 20; n++)
       {  
           
           a=1.0; b=2.0;
           cout  << n << " ";
           p = 1 - pow(10.0, (-n));
           
           s1 = (pow(b, (1 - p)) - (pow(a, (1 - p))))/(1 - p);
           cout <<s1<<" " << endl;
           PLIK<<s1<<setprecision(16)<<" "<<endl;
           
       }
     
       
       PLIK<<"ANALYTICALLY B"<<endl;
       cout << "ANALYTICALLY " << endl;
       cout << "SECTION B:" << endl; // Podpunkt drugii
       for (n = 1; n <= 20; n++)
       {
           a=1.0; p=0.5;
           cout << n << " ";
           b = 1 + pow(10.0, (-n));
           
           s2 = (pow(b, (1 - p)) - (pow(a, (1 - p))))/(1 - p);
           cout << s2<<" " << endl;
           PLIK<<s2<<setprecision(16)<<" "<<endl;
           
       }
       
     
       
       PLIK<<"SIMPSON A"<<endl;
       cout << "SIMPSON RULE" << endl;
       cout << "SECTION A" << endl;
       
       for (n = 1; n <= 20; n++)
       {  
           p=1 - (pow(10.0, (-n)));
           a=1.0;
           cout  << n << " ";
           b=2.0;
           
           s3 = (b-a)/ 6 * (f(a) + (4*(f((a+b)/2)))+f(b));
           cout << s3<<" " << endl;
           PLIK<<s3<<setprecision(16)<<" "<<endl;
           
       }
     
       
       
       PLIK<<"SIMPSON B"<<endl;
       cout << "SIMPSON RULE " << endl;
       cout << "SECTION B" << endl;
       
       
       for (n = 1; n <= 20; n++)
       {  
           a=1.0;p=0.5;
           cout << n << " ";
           b=1 + pow(10.0, (-n));
         
           s4 = (b-a)/ 6 * (fx(a) + (4*(fx((a+b)/2)))+fx(b));
           cout <<  s4 << " "  << endl;
           PLIK<<s4<<setprecision(16)<<" "<<endl;
           
       }
     
       PLIK.close();
       
       cout<<endl;

December 6th, 2012, 06:19 AM

salem

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Integral calculus using analytically and Simpson methods

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