Runge-Kutta Family of Methods to Solve First-Order Ordinary Differential Equations

Overview

This repository contains implementations of the Runge-Kutta family of methods to solve systems of first-order ordinary differential equations (ODEs). These methods are widely used in numerical analysis for solving initial value problems.

Methods Implemented

• Euler Method (1st Order)
• RK2 (Runge-Kutta 2nd Order Method)
• RK4 (Runge-Kutta 4th Order Method)

Files

• euler.py: Implementation of the Euler method.
• RK2.py: Implementation of the RK2 method.
• RK4.py: Implementation of the RK4 method.
• main.py: Example usage of the implemented methods.
• README.md: This file.
• .gitignore: Git ignore file to exclude unnecessary files from the repository.

Usage

To use any of the methods, import the corresponding module and call the function with the appropriate parameters. For example, to use the RK4 method:

from RK4 import RK4

# Define the system of ODEs
def f(t, y):
    dydt = -2 * t * y
    return dydt

# Initial conditions
t0 = 0
y0 = 1
t_end = 2
h = 0.1

# Solve the ODE
t_values, y_values = rk4(f, t0, y0, t_end, h)

Alternatively, execute the main.py script to run the example provided.

Requirements

• Python 3.x
• NumPy (for numerical operations)
• Pandas (for handling data in a tabular format)

Installation

Clone the repository and navigate to the directory:

git clone https://github.com/yourusername/runge-kutta-methods.git
cd runge-kutta-methods

Install the required packages:

pip install numpy
pip install matplotlib pandas

Acknowledgements

This project was developed as part of the Mathematical Methods in Aerospace Engineering [AE 601] course at the Indian Institute of Space Science and Technology.