Numerical-PDE

This Repository contains a collection of MATLAB code to implement finite difference schemes to solve partial differential equations. These codes were written as a part of the Numerical Methods for PDE course in BITS Pilani, Goa Campus.

1. Parabolic PDE

   • Method of Lines
   • Forward Euler
   • Backward Euler
   • Crank Nicolson Method
   • ADI Method
   • Nonlinear PDE

2. Elliptic PDE

   • Jacobi Iterative Scheme
   • Gauss Seidel Iterative Scheme
   • SOR

3. Practice

   • A summary of all the schemes implemented so far in the course

4. Project Code

   • Assignment 1
     • Numerics of the viscous Burger's Equation.
       • Common Schemes like Backward Euler, Godunov, Einguist Osher, Lax Friedrich are implemented
       • Order of Convergence of the Schemes
   • Assignment 2
     • Fast Fourier Methods to solve Elliptic PDE
       • FFT : Compares the Slow Fourier Transform with the Cooley Tukey Algorithm.
       • Final Code : Implementation of FFT for solving Poisson Equations with Dirichlet and Neumann Boundary Conditions.

5. Others

   • Numerics of the Korteweg-de-Vries equation

       * Upwind scheme
       * Backward Euler Scheme
       * Zabusky Kruskal Scheme
       * Crank Nicolson Scheme