# Finite Difference Methods
## Overview
This repository showcases two MATLAB projects that illustrate the use of finite difference methods:
1. **Laplace's Equation Solver:** Utilizes the finite difference method (FDM) to solve Laplace's equation on a 2D grid, helping to determine the potential distribution within a rectangular domain under given boundary conditions.
2. **Finite Difference Time Domain (FDTD) Simulation:** Applies the FDTD method to solve Maxwell's equations in a one-dimensional domain, incorporating Mur's absorbing boundary conditions to simulate wave propagation and absorption.
These projects aim to enhance practical understanding of numerical methods and their applications in computational physics.
## Project Structure
The repository includes the following files:
* `laplace_solver.m` - MATLAB script to solve Laplace's equation using the finite difference method.
* `EM_wave_simulator.m` - MATLAB script to solve Maxwell's equations using the finite difference time domain method.
* `README.md`- This file
## Features
### Laplace's Equation Solver
* Solves Laplace's equation using a finite difference grid.
* Supports user-defined boundary conditions for the grid edges.
* Visualizes potential distribution through a 3D surface plot.
### Finite Difference Time Domain (FDTD) Simulation
* Solves Maxwell's equations in a 1D domain with the FDTD leap-frog scheme.
* Implements Mur's absorbing boundary conditions for wave absorption.
* Visualizes electric and magnetic field intensities over time.
## Technologies Used
* **MATLAB:** The main programming environment for implementing finite difference methods and simulations.
* **MATLAB Plotting Functions:** Used for result visualization and field distribution plots.
## Important Notes
1. Ensure MATLAB is installed and configured correctly to run the scripts.
2. Adjust grid resolution and simulation parameters in the scripts to fit different problem sizes and requirements.
3. For theoretical background and detailed explanations, refer to the [Documentation](https://docs.google.com/presentation/d/1ynMJxYFonx6eQYAnlvbByBCSkSBgZWrh/edit?usp=sharing&ouid=112652190702611863831&rtpof=true&sd=true).
## ð About Me
My name is __Sangeet,__ and I am currently pursuing __BTech in Computer Science and Engineering at IIT Jammu__. This project uses finite difference methods to solve Laplace's equation and Maxwell's equations, and it attempts to improve my grasp of numerical methods.
## ð Links
[](https://www.linkedin.com/in/sangeet-sangwan-090196258/)
