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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