Question

Write a program in Java to find the roots of the equation

x^3 - 18 = 0 Using the bisection method and Newton-Raphson Method.

Compare the two solutions.

Answer 1

Bisection Method

public class Main {
    static final float EPSILON = (float)0.01;

    static double func(double x)
    {
        return x*x*x - 18;
    }

    static void bisection(double a, double b)
    {
        if (func(a) * func(b) >= 0)
        {
            System.out.println("You have not assumed right a and b");
            return;
        }

        double c = a;
        while ((b-a) >= EPSILON)
        {
            c = (a+b)/2;

            if (func(c) == 0.0)
                break;

            else if (func(c)*func(a) < 0)
                b = c;
            else
                a = c;
        }
        System.out.printf("The value of root is : %.4f", c);
    }

    public static void main(String[] args)
    {
        double a =-200, b = 300;
        bisection(a, b);
    }
}

Newton-Raphson

public class Main {
    static final float EPSILON = (float)0.01;

    static double func(double x)
    {
        return x * x * x - 18;
    }

    static double derivFunc(double x)
    {
        return 3 * x * x;
    }

    static void newtonRaphson(double x)
    {
        double h = func(x) / derivFunc(x);
        while (Math.abs(h) >= EPSILON)
        {
            h = func(x) / derivFunc(x);

            x = x - h;
        }

        System.out.print("The value of the root is : " + Math.round(x * 100.0) / 100.0);
    }

    public static void main (String[] args)
    {
        double x0 = -20;
        newtonRaphson(x0);
    }
}