This script provides solutions to a variety of numerical methods problems using Python. It includes implementations of the Euler and Runge-Kutta methods for solving ordinary differential equations, Gaussian elimination with backward substitution for solving linear systems, LU Factorization, and checks for matrix properties (diagonally dominant and positive definite).

• Euler method for solving differential equations
• 4th-order Runge-Kutta method
• Gaussian elimination and backward substitution
• LU Factorization using SciPy
• Matrix property checks: diagonally dominant and positive definit

Requirements instructions will be found in the requirements.txt file in the repository

To use the script, simply run it in your preferred Python environment. The script is self-contained and does not require any additional input once the initial conditions are set within the script.

python main.py

The script is divided into several function definitions followed by their execution. The results are printed to the console.

• Euler and Runge-Kutta Methods: Solve the specified differential equation.
• Gaussian Elimination: Solve the linear system represented by the augmented matrix.
• LU Factorization: Perform factorization on a given matrix and print the L, U, and determinant.
• Matrix Property Checks: Print out whether a matrix is diagonally dominant or positive definite.