#include <iostream>
#include <cmath>
#include <iomanip>
#include <fstream>
using namespace std;
double f(double x) {
if(x==0.0){
return 1.0; }
return sin(x) / x;
}
double trapezoidal(double a, double b, int n) {
double h = (b - a) / n;
double sum = 0.5 * (f(a) + f(b));
for (int i = 1; i < n; ++i) {
sum += f(a + i * h);
}
return h * sum;
}
double richardson(double T1, double T2) {
return (4 * T2 - T1) / 3;
}
double romberg(double a, double b, int maxLevel) {
const int N = maxLevel + 1;
double R[N][N];
for (int i = 0; i <= maxLevel; ++i) {
int n = pow(2, i);
R[i][0] = trapezoidal(a, b, n);
for (int k = 1; k <= i; ++k) {
R[i][k] = (pow(4, k) * R[i][k - 1] - R[i - 1][k - 1]) / (pow(4, k) - 1);
}
}
return R[maxLevel][maxLevel];
}
int main() {
ofstream file1("ass13.txt");
double a = 0.0, b = 1.0;
cout << fixed << setprecision(10);
double reference = 0.9460830703671831;
int steps[] = {10, 20,30,40,50,60,70,80,90,100,110,120,130,140};
cout << "Trapezoidal Approximations:\n";
for (int n : steps) {
double h = 1.0 / n;
double result = trapezoidal(a, b, n);
double error = abs (reference - result);
cout << "n = " << n << ", I ≈ " << result << endl;
double T1 = trapezoidal(a, b, n);
double T2 = trapezoidal(a, b, 2*n);
double R = richardson(T1, T2);
double error1 = abs(reference - R);
cout << "\nRichardson Extrapolation I ≈ " << R << endl;
double romberg_result = romberg(a, b, 4);
double error2 = abs(reference - romberg_result);
cout << "\nRomberg Integration (R[4][4]): I ≈ " << romberg_result << endl;
file1 << log(h) << " " << log(error) << " " << log(error1) << " " << log(error2) << endl;
}
file1.close();
return 0;
}

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