Finite Difference Methods for Partial Differential Equations

This repo implements basic finite difference methods for solving Partial Differential Equations (PDEs). Examples are taken from this book:

Smith, G.D., Smith, G.D. and Smith, G.D.S., 1985. Numerical solution of partial differential equations: finite difference methods. Oxford university press.

Requirements

• Python
• Numpy
• Matplotlib
• Seaborn
• Tabulate

Details

• Each notebook contains an example (or part of it) based on the book structure.
• Two different animated plots have been drawn for each example.
• Both simple and vectorized implementations are available for each example.

Notebooks

• Example 2.1: Explicit discretization with various step sizes:
  • Case 1: r = 0.1
  • Case 2: r = 0.5
  • Case 3: r = 1.0
• Example 2.2: Crank-Nicolson implicit discretization.
• Example 2.3: Explicit discretization with Neumann boundary conditions (Central Difference).
• Example 2.4: Explicit discretization with Neumann boundary conditions (Forward Difference).
• Example 2.5: Crank-Nicolson discretization with Neumann boundary conditions.