Методы вычислений 25.11.22

#define _USE_MATH_DEFINES
#include <iostream>
#include <iomanip>
#include <vector>
#include <random>
#include <chrono>
#include <cmath>
#include <ctime>
using namespace std;
using namespace chrono;

typedef vector <double> vec;
typedef vector <vec> mat;

const double v = 10;

double y_correct(double x)
{
    return x * x * x * (x - v);
}

double f(double x, double y)
{
    return 3 * y / x + (x * x * x);
}

void left_rectangular(double a, double b, double h)
{
    // начальные условия
    double x0 = v, y0 = 0, EPS = 1e-9;

    vec x, y;

    do
    {
        x.push_back(x0);
        y.push_back(y0);

        // формула из соотношений (5)
        y0 += h * f(x0, y0);
        x0 += h;

    } while (x0 <= b + EPS);

    cout << "+-----------------------------------------------------------------------------------+\n";
    cout << "| Формула левых прямоугольников на отрезке [" << a << ", " << b << "] c шагом h = " << h << " |\n";
    cout << "+-----------------------------------------------------------------------------------+\n\n";

    cout << left << "+------------+-------------+\n";
    cout << left << "|    x[i]    |    delta    |\n";
    cout << left << "+------------+-------------+\n";

    for (int i = 0; i < x.size(); ++i)
        cout << left << "| " << setw(10) << x[i] << " | " << setw(11) << fabs(y[i] - y_correct(x[i])) << " |\n";

    cout << left << "+------------+-------------+\n\n";
}

void mid_rectangular(double a, double b, double h)
{
    // начальные условия
    double x0 = v, y0 = 0, x_tmp = x0 + h / 2, y_tmp = h / 2 * f(x0, y0), EPS = 1e-9;

    vec x, y;

    do
    {
        x.push_back(x0);
        y.push_back(y0);

        // формулы из соотношений (6, 7)
        y0 += h * f(x_tmp, y_tmp);
        x0 += h;

        x_tmp += h;
        y_tmp = y0 + h / 2 * f(x0, y0);

    } while (x0 <= b + EPS);

    cout << "+-------------------------------------------------------------------------------------+\n";
    cout << "| Формула средних прямоугольников на отрезке [" << a << ", " << b << "] c шагом h = " << h << " |\n";
    cout << "+-------------------------------------------------------------------------------------+\n\n";

    cout << left << "+------------+-------------+\n";
    cout << left << "|    x[i]    |    delta    |\n";
    cout << left << "+------------+-------------+\n";

    for (int i = 0; i < x.size(); ++i)
        cout << left << "| " << setw(10) << x[i] << " | " << setw(11) << fabs(y[i] - y_correct(x[i])) << " |\n";

    cout << left << "+------------+-------------+\n\n";
}

void trapezoid(double a, double b, double h)
{
    // начальные условия
    double x0 = v, y0 = 0, x_tmp = x0 + h, y_tmp = h * f(x0, y0), EPS = 1e-9;

    vec x, y;

    do
    {
        x.push_back(x0);
        y.push_back(y0);

        // формулы из соотношений (5, 9)
        y0 += h * (f(x0, y0) + f(x_tmp, y_tmp)) / 2;
        x0 += h;

        x_tmp += h;
        y_tmp = y0 + h * f(x0, y0);

    } while (x0 <= b + EPS);

    cout << "+----------------------------------------------------------------------+\n";
    cout << "| Формула трапеций на отрезке [" << a << ", " << b << "] c шагом h = " << h << " |\n";
    cout << "+----------------------------------------------------------------------+\n\n";

    cout << left << "+------------+-------------+\n";
    cout << left << "|    x[i]    |    delta    |\n";
    cout << left << "+------------+-------------+\n";

    for (int i = 0; i < x.size(); ++i)
        cout << left << "| " << setw(10) << x[i] << " | " << setw(11) << fabs(y[i] - y_correct(x[i])) << " |\n";

    cout << left << "+------------+-------------+\n\n";
}

int main()
{
    setlocale(LC_ALL, "Russian");
    cout << fixed << setprecision(5);

    double a = v, b = v + 5, h = 0.1;

    left_rectangular(a, b, h);
    mid_rectangular(a, b, h);
    trapezoid(a, b, h);

    return 0;
}