How I can write this numericah method program

1. Drawing.
2. Fixed point iteration.
3. Bisection.
4. Newton Raphson.
5. False position.
B-Interpolation and extrapolation by the next methods:
a. Newton forward.
b. Newton backward.
c. Lagrange method.
d. Splines.

import java.util.Scanner;

public class RootInterpExtrap {

    // Function to perform false position root finding
    public static double falsePosition(double f(double), double a, double b, double tol, int maxIter) {
        double fa = f(a);
        double fb = f(b);
        double c = a;
        for (int i = 0; i < maxIter; i++) {
            c = (a * fb - b * fa) / (fb - fa);
            double fc = f(c);
            if (fc == 0 || (b-a)/2 < tol) {
                break;
            }
            if (fc * fb < 0) {
                fa = fb;
                a = b;
            } else {
                fa = fc;
            }
            b = c;
            fb = fc;
        }
        return c;
    }

    // Function to perform spline interpolation and extrapolation
    public static double spline(double[] x, double[] y, double x0) {
        int n = x.length;
        double[] h = new double[n-1];
        double[] b = new double[n-1];
        double[] u = new double[n-1];
        double[] v = new double[n-1];
        for (int i = 0; i < n-1; i++) {
            h[i] = x[i+1] - x[i];
            b[i] = (y[i+1] - y[i]) / h[i];
        }
        u[1] = 2 * (h[0] + h[1]);
        v[1] = 6 * (b[1] - b[0]);
        for (int i = 2; i < n-1; i++) {
            u[i] = 2 * (h[i-1] + h[i]) - (h[i-1]*h[i-1]) / u[i-1];
            v[i] = 6 * (b[i] - b[i-1]) - (h[i-1]*v[i-1]) / u[i-1];
        }
        double[] z = new double[n];
        for (int i = n-2; i > 0; i--) {
            z[i] = (v[i] - h[i]*z[i+1]) / u[i];
        }
        z[0] = 0;
        z[n-1] = 0;
        int j = 0;
        for (int i = 1; i < n; i++) {
            if (x[i] > x0) {
                j = i-1;
                break;
            }
        }
        double hj = x[j+1] - x[j];
        double aj = (x[j+1] - x0) / hj;
        double bj = (x0 - x[j]) / hj;
        double cj = (aj*aj*aj - aj)*hj*hj / 6;
        double dj = (bj*bj*bj - bj)*hj*hj / 6;
        return aj*y[j] + bj*y[j+1] + cj*z[j] + dj*z[j+1];
    }

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);
        boolean running = true;
        while (running) {
            System.out.println("Select a method:");