https://github.com/nickklos10/cot-4500-as3
Solutions to a variety of numerical methods problems using Python
https://github.com/nickklos10/cot-4500-as3
euler-method gaussian-elimination-algorithm lu-factorization matrix-algebra runge-kutta-methods
Last synced: 2 months ago
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Solutions to a variety of numerical methods problems using Python
- Host: GitHub
- URL: https://github.com/nickklos10/cot-4500-as3
- Owner: nickklos10
- Created: 2024-03-29T14:01:29.000Z (about 1 year ago)
- Default Branch: main
- Last Pushed: 2024-03-29T14:10:44.000Z (about 1 year ago)
- Last Synced: 2025-01-18T02:27:57.238Z (4 months ago)
- Topics: euler-method, gaussian-elimination-algorithm, lu-factorization, matrix-algebra, runge-kutta-methods
- Language: Python
- Homepage:
- Size: 5.86 KB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Numerical Methods Script
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).
### Features
- 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
Requirements instructions will be found in the requirements.txt file in the repository
### Running the script
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
### Structure
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.