LastMethods

#include <iostream>

using namespace std;

double function(double x);
double fi(double x);
double derivative(double x);
double derivative_2(double x);
int check_for_newton(double a, double b);
void simple_iteration();
void method_chord();
void method_newton();
void method_chebishev();
bool sign(double a);

int main() {
    int menu = 0;
    cout << "Choice method:\n1.Method Simple Iteration\n2.Method Chord\n3.Method Newton\n4.Method Chebishev\nEnter:"; cin >> menu;
    if (menu == 1) {
        simple_iteration();
    }
    if (menu == 2) { method_chord(); }
    if (menu == 3) { method_newton(); }
    if (menu == 4) { method_chebishev(); }
    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));

}


void method_newton()
{
    double a, b, eps;
    int n = 0;
    cout << "~~~~~Method Newton~~~~~" << endl;
    cout << "Enter left border: "; cin >> a;
    cout << "Enter right border: "; cin >> b;
    cout << "Enter epsilon: "; cin >> eps;
    double x_i, x = 0;
    if (check_for_newton(a, b) == -1)
    {
        x = a;
        cout << "As x0 we take the left border\n";
    }
    else if (check_for_newton(a, b) == 1)
    {
        x = b;
        cout << "As x0 we take the right border\n";
    }

    cout << "Function(a) * Derivative^2(a) = " << function(a) * derivative_2(a) << endl;
    cout << "Function(b) * Derivative^2(b) = " << function(b) * derivative_2(b) << endl;
    cout << "X0 = " << x << endl;

    do {
        x_i = x;
        x = x_i - (function(x_i)) / derivative(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: %1.15f\n", function(x));
}


void method_chebishev()
{
    double a, b, eps;
    int n = 0;
    cout << "~~~~~Method Chebishev~~~~~" << endl;
    cout << "Enter left border: "; cin >> a;
    cout << "Enter right border: "; cin >> b;
    cout << "Enter epsilon: "; cin >> eps;
    double x_i, x = 0;
    if (check_for_newton(a, b) == -1)
    {
        x = a;
        cout << "As x0 we take the left border\n";
    }
    else if (check_for_newton(a, b) == 1)
    {
        x = b;
        cout << "As x0 we take the right border\n";
    }

    cout << "Function(a) * Derivative^2(a) = " << function(a) * derivative_2(a) << endl;
    cout << "Function(b) * Derivative^2(b) = " << function(b) * derivative_2(b) << endl;
    cout << "X0 = " << x << endl;

    do {
        x_i = x;
        //x = x_i - ((function(x_i)) / derivative(x_i)) - ((derivative_2(x_i) * pow(function(x_i),2)) / (2 * pow(derivative(x_i), 3)));
        x = x_i - ((function(x_i)) / derivative(x_i)) - ((derivative_2(x_i) * function(x_i) * function(x_i)) / (2 * pow(derivative(x_i), 3)));

        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;
}

double derivative(double x)
{
    return 3 * pow(x, 2) + 3;
}


double derivative_2(double x)
{
    return 6 * x;
}


int check_for_newton(double a, double b)
{
    if (function(a) * derivative_2(a) > 0)return -1;
    else if (function(b) * derivative_2(b) > 0)return 1;
    else return 0;
}