Numerical PDE Techniques for Scientists and Engineers

by: Prof. Dinshaw S. Balsara

Chapter 2: Finite Difference Approximations

• Abstract
• Movies
• Slides with Voice-Over
• Chapters, Codes, Etc
• Textbook Home

Movies

The following video lectures are available for this chapter. Please use Chrome or Firefox to download the movies to your disk. Then play the movies with VLC.

• 2.1) Introduction
• 2.2) Meshes and Discretization on a Mesh (Video 1, Video 2)
• 2.3) Taylor Series and Accuracy of Discretizations
• 2.4) Finite Difference Approximations and Their Consistency
• 2.5) The Stability of Finite Difference Approximations
• 2.6) von Neumann Stability Analysis for Linear Parabolic Equations
  • 2.6.1) Stability Analysis for Time-explicit Linear Parabolic Equations
  • 2.6.2) Stability Analysis for Time-implicit and Semi-implicit Linear Parabolic Equations
  • 2.6.3) Stability Analysis for the Time-implicit TR-BDF2 Method
  • 2.6.4) Boundary Conditions for Parabolic Equations
  • 2.6.5) Introduction to Matrix Methods for Parabolic Equations
• 2.7) von Neumann Stability Analysis of Linear Hyperbolic Equations
  • 2.7.1) Forward Euler Scheme (Never Used)
  • 2.7.2) Lax-Friedrichs Scheme
  • 2.7.3) The Lax-Wendroff Scheme
  • 2.7.4) The Two-stage Runge-Kutta Scheme
  • 2.7.5) First Order Accurate Upwind Scheme (i.e. Donor Cell Scheme)
  • 2.7.6) Section Summary for Hyperbolic Equations

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