Welcome to my repository where I explore the fascinating world of physics using numerical methods in Julia.🌠💻
Here I am learning to bridge the gap between the theroetical physics and its real-life applications using computational techniques.
I am happy to show some of my most interesting projects related to heat transfer with heat generation, particle motion analysis, and Haley's Comet simulation. 💗
- Numerical differentiation and integration for first and higher-order differential equations.
- Solving non-linear systems using Newton's Method.
- Analysis and solving both Initial Value Problems (IVPs) and Boundary Value Problems (BVPs).
Boundary Value Problems
Currently there are two Boundary Value Problem projects related to heat transfer:
- Heat generation in a cylindrical wire (solved using Euler Method)
- Spherical object with heat generation (solved using Newton-Raphson Method for nonlinear systems)
Initial Value Problems
This folder contains the following methods and areas of application:
- Solving first and second order ODE's using Euler Method to demonstrate its simplicity for numerical integration and set the base for understanding more complex methods.
- Particle Motion Initial Value Problem (using Euler Method for finding the velocity and position of a particle at the next time step)
- Haley's Comet Trajectory and Velocity Simulation (using second order Taylor expansion).
Every code is carefully commented and the results are visualized and documented along the way. In the future I hope to include more heat transfer and fluid dynamics - related projects as these are areas I am also highly interested in. I also wish to expand my knowledge of particle physics to be able to simulate particle decays and their detected trajectories.
- Book: An Introduction to Computational Physics by Tao Pang
- Online notes: Numerical Methods for Engineers by Jeffrey R. Chasnov
This repository reflects my passion for computational physics and my commitment to building a solid foundation in numerical analysis. I hope you find these implementations insightful and inspiring! ✨