NewMethods

#include <iostream>

using namespace std;

double function(double x);
double fi(double x);
void simple_iteration();
void method_chord();
bool sign(double a);

int main() {
    int menu = 0;
    cout << "Choice method:\n1.Method Simple Iteration\n2.Method Chord\nEnter:"; cin >> menu;
    if (menu == 1) {
        simple_iteration();
    }
    if (menu == 2) { method_chord(); }
    return 0;
}

double function(double x) {
    return pow(x, 3) + 3 * x + 1;
}

double fi(double x) {
    return (-1 - pow(x, 3) / 3);
}

void simple_iteration() {
    double a, b, eps;
    int n = 0;
    cout << "~~~~~Method Simple Iteration~~~~~" << endl;
    cout << "Enter left border: "; cin >> a;
    cout << "Enter right border: "; cin >> b;
    cout << "Enter epsilon: "; cin >> eps;
    double x_i, x = a;

    do
    {
        x_i = x;
        x = fi(x_i);
        n++;
    } while (fabs(x_i - x) >= eps);

    cout << endl << "Root of the equation: " << x << endl;
    cout << "Count of iterations: " << n << endl;
    printf("Checking the resultating root: %1.10f\n", function(x));

}

void method_chord()
{
    double a, b, eps;
    int n = 0;
    cout << "~~~~~Method Chord~~~~~" << endl;
    cout << "Enter left border: "; cin >> a;
    cout << "Enter right border: "; cin >> b;
    cout << "Enter epsilon: "; cin >> eps;
    double x_i, x = a;

    if (sign(a) == true)
    {
        x = b;
        do
        {
            x_i = x;
            x = x_i - ((function(x_i)) / (function(x_i) - function(a))) * (x_i - a);
            n++;
        } while (fabs(x_i - x) >= eps);
    }
    else
    {
        x = a;
        do
        {
            x_i = x;
            x = x_i - ((function(x_i)) / (function(x_i) - function(b))) * (x_i - b);
            n++;
        } while (fabs(x_i - x) >= eps);
    }

    cout << endl << "Root of the equation: " << x << endl;
    cout << "Count of iterations: " << n << endl;
    printf("Checking the resultating root: %1.10f\n", function(x));

}

bool sign(double a)
{
    if (function(a) > 0) return true;
    else if (function(a) < 0) return false;
}