lab4.cpp

using namespace std;

#include <vector>
#include <cstdio>
#include <cmath>

double f(double x) {
    return 1.0 / x;
}

double F(double x) {
    return log(x);
}

double Integral(double a, double b, int n) {
    double sigma1 = 0, sigma2 = 0;

    double h = (b - a) / n;
    for (int i = 1; i < n; i++) {
        if (i % 2 == 0) sigma2 += f(a + i * h);
        else sigma1 += f(a + i * h);
    }
    return h / 3 * (f(a) + f(b) + 4 * sigma1 + 2 * sigma2);
}

int main() {
    double errors[6], a = 1, b = 375, I = F(b) - F(a);

    int M = 29;

    printf("a = %g\nb = %g\n", a, b);
    printf("I = F(b) - F(a) = %g\n", I);
    printf("M = %d\n", a, b, I, M);

    printf("\nSimpson method\n");
    printf("| given error | integration step |  integral value  | received error |\n");

    double q = 180 / ((b - a) * M);
    int i = 0;
    for (double eps = 1e-2; eps >= 1e-12; eps *= 1e-2) {
        int n = 2 * ceil((b - a) / pow(eps * q, 0.25) / 2.0);

        double integral = Integral(a, b, n);
        double error = fabs(I - integral);
        errors[i++] = error;

        printf("| %.5e | %.10e | %14.14f | %.8e |\n", eps, (b - a) / n, integral, error);
    }
    printf("\nRunge method\n");
    printf("| given error | integration step | received error |\n");

    for (int i = 0; i < 6; i++) {
        double error = errors[i];

        int n = 2 * ceil((b - a) / pow(error, 0.25) / 2.0);
        double h = (b - a) / n;

        double R = 0, In, I2n = Integral(a, b, n);
        do {
            In = I2n;
            I2n = Integral(a, b, n *= 2);
            R = fabs(In - I2n) / 15;
        } while (R > error);

        printf("| %.5e | %.10e | %.8e |\n", error, h, R);
    }
}