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Session 14
Numerical Methods

Partial Differential Equations: Finite Difference Methods

5 hours
Duration
8
Materials
6
Objectives
Session Overview

Numerical solution of partial differential equations using finite difference methods. Elliptic, parabolic, and hyperbolic PDEs with stability and convergence analysis.

Learning Objectives
By the end of this session, you should be able to:
  • Discretize elliptic PDEs using finite difference schemes
  • Implement explicit and implicit methods for parabolic PDEs
  • Master stability analysis using von Neumann method
  • Apply finite difference methods to hyperbolic PDEs
  • Understand CFL condition and numerical stability requirements
  • Solve heat equation, wave equation, and Laplace equation numerically
Course Materials
Download materials for offline study and reference
PDE Theory and Classification (50 pages)
Available material
Finite Difference Scheme Derivations
Available material
Stability Analysis Methods and Criteria
Available material
Heat Equation Implementation (Explicit/Implicit)
Available material
Wave Equation Finite Difference Solutions
Available material
Elliptic PDE Solver Development
Available material
CFL Condition Analysis and Applications
Available material
Engineering PDE Applications Project
Available material