Simpson's Rule for nth number of interval

[Danjes]

My objective is to estimate the numerical integral method using Simpson's rule for n numbers of interval and n = 2,4,6,8,....20) and output should be given in three columns which are n , S (Simpson's result) and E (Error)

#include<stdio.h>
#include <iostream>
#include<cmath>

double f(double x)
 {
 double g =(400*x*x*x*x*x -900*x*x*x*x + 675*x*x*x-200*x*x+25*x+0.2);

   return g;
}

   int main ()
{
 int i ;

long double a = 0,b = 0.8,h,n, sum , S, E, L = 1.640533; // L is exact  result value of the given function  integration 
double x[10], y[10];
double x[n],y[n];

cout <<" Given f(x)= 400x^5 -900x^4+675^x^3+ -200x^2+25x-0.2 "<<endl;



  for (n=2; n< 21;n+=2){
  for (i=0;i<n+1;i++){


    h=(b-a)/n;
    x[i]=a+i*h;
    y[i]=f(x[i]);
  }

  }

for (i=1;i<n;i+=2)
{
sum = sum+4*y[i];
}
for (i=2;i<n-1;i+=2)
{
sum1=sum1+2*y[i];
}
    S = h/3*(y[0]+y[n]+sum);
   E = ((L-S)/L)*100;



cout << "  " << n << "  " << S << "  "  << E << "     "  << endl;

 return 0 ;

 }

[lastchance]

Please @Danjes, DON'T START A NEW THREAD ON THE SAME TOPIC - it confuses everything.

double x[10], y[10];
double x[n],y[n];

Does this not look wrong to you?
Irrespective of the C++ errors here, you do NOT need arrays at all. Please read below.


You have an n-loop enclosing an i-loop on lines 25-34. Both of these close, but you do not need this segment of code at all (except for the h=(b-a)/n; line which can be moved to later).


You need an n loop to enclose lines lines 36 to 49. It should start with the interval calculation h=(b-a)/n;. That should be followed by re-setting sum to zero for each value of n.


You are confusing sum and sum1. I think they are the same variable.


Instead of using your y-array on line 38 you can evaluate the function here - it is only used once:
sum = sum+4*f( a+i*h );
Something similar can be done on line 42.


There appears to be a minor discrepancy (+0.2 or -0.2) between the function calculated on line 8 and that stated on line 21. Only you know which is correct.


PLEASE USE CONSISTENT AND SENSIBLE INDENTATION. Look at your code in tags above.