lab4

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

double f(double x) {
    return (cos(x) - x * sin(x)) / pow(cos(x), 2);
}

double F(double x) {
    return -x / cos(x) - 2 * log(cos(x * 0.5) - sin(x * 0.5)) + 2 * log(sin(x * 0.5) + cos(x * 0.5));
}

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

    double h = (b - a) / (double) 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 / 3.0 * (f(a) + f(b) + 4.0 * sigma1 + 2.0 * sigma2);
}

int main() {
    std::vector<double> errors;

    double a = -1.5;
    double b = 1.5;
    double I = F(b) - F(a);

    double q = 180.0 / ((b - a) * 20000000.0);

    printf("\nsimpson\n| given error |       step       |       value       | received error |\n");
    for (double eps = 1e-2; eps >= 1e-12; eps *= 1e-2) {
        int n = (int((b - a) / pow(eps * q, 0.25)) >> 1) << 1;

        double value = myintegral(a, b, n);
        errors.push_back(fabs(I - value));

        printf("| %.5e | %.10e | %13.13f | %.8e |\n", eps, (b - a) / (double) n, value, errors.back());
    }
    printf("\nrunge\n| given error |       step       | received error |\n");

    for (const double &error : errors) {
        int n = (int((b - a) / pow(error, 0.25)) >> 1) << 1;

        double R = 0;
        double I2n = myintegral(a, b, n);
        do {
            double In = I2n;
            I2n = myintegral(a, b, n <<= 1);
            R = fabs(In - I2n) / 15.0;
        } while (R > error);

        printf("| %.5e | %.10e | %.8e |\n", error, (b - a) / (double)n, R);
    }
    return 0;
}