/Newton-Raphson-Method-Program

Primary LanguagePython

Newton-Raphson Method Implementation

This repository contains a Python implementation of the Newton-Raphson method for finding the root of a given function. The function used in this implementation is ( f(x) = 4x^3 - 15x^2 + 17x - 16 ).

Overview

The Newton-Raphson method is an iterative numerical technique for finding approximate solutions to equations of the form ( f(x) = 0 ). This implementation includes the main algorithm, a function to compute the derivative of ( f(x) ), and a plotting function to visualize the iterations.

Files

  • main.py: Contains the implementation of the Newton-Raphson method and the plotting functions.

Usage

  1. Clone the repository:

    git clone <repository-url>
cd <repository-directory>

  2. Run the program:

    python main.py

  3. Input: When prompted, enter an initial guess for the root.

Functions

f(x) Defines the function for which the root is to be found.

def f(x):
    return 4 * x**3 - 15 * x**2 + 17 * x - 16

f_derivative(x) Defines the derivative of the function ( f(x) ).

def f_derivative(x):
    return 12 * x**2 - 30 * x + 17

newtonRaphson(x0) Implements the Newton-Raphson method.

  • Parameters: x0 (float) - initial guess.
  • Returns: root (float) - estimated root, x_values (list of float) - x values of each iteration, y_values (list of float) - corresponding y values.
def newtonRaphson(x0):
    # Implementation details
    return root, x_values, y_values

plot_function_and_iterations(x_values, y_values) Plots the function and the iterations of the Newton-Raphson method.

  • Parameters: x_values (list of float) - x values of each iteration, y_values (list of float) - corresponding y values.
def plot_function_and_iterations(x_values, y_values):
    # Implementation details

Example Output

Upon running the program, the user is prompted to input an initial guess. The program then iteratively applies the Newton-Raphson method, printing each iteration's value and finally plotting the function along with the iterations.

Masukkan tebakan awal: 2

Iterasi ke-0: x = 2.0 Iterasi ke-1: x = 1.75 Iterasi ke-2: x = 1.6104651162790698 ... Akar persamaan adalah: 1.528013758419482

The plot will show the function ( f(x) ) and the iterations of the Newton-Raphson method.

Requirements

  • Python 3.x
  • NumPy
  • Matplotlib

Install the required packages using:

pip install numpy matplotlib