MATH 5474 (CS 5474)
FINITE DIFFERENCE METHODS
FOR PARTIAL DIFFERENTIAL EQUATIONS

Lecture: Tuesday-Thursday 2pm-3:15pm in McBryde 302

Instructor: C. Beattie (beattie@math.vt.edu),

Office: 552 McBryde Hall     Phone: 231-8279

Office Hours: 11am-12:30pm Wed & by appointment

Course Description: The finite difference method is the basis for many efficient numerical approaches for approximating solutions to differential equations that arise in areas as varied as electrodynamics, elasticity theory, fluid mechanics, gas dynamics, particle and radiation transfer, atmosphere and ocean dynamics, and plasma physics.

This course provides an introduction to the analysis of finite difference methods and their extensions. Topics include:

• Analysis of basic finite difference methods (consistency, stability, convergence, dispersion, dissipation).
• Time-stepping and the method of lines (linear multistep methods, Runge-Kutta and SIRK methods, stiffness)
• Spectral/pseudospectral methods

Prerequisites: 3414 and 4525 or equivalent advanced calculus preparation. An advanced undergraduate course in numerical analysis is recommended but not required. Computing assignments will be done with the aid of Matlab.

Text Resources: The following books are available electronically through University Libraries at the associated links; print copies of items (2), (3), and (4) are on reserve in Newman.

1. Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, by Lloyd N. Trefethen
2. Finite Difference Schemes and Partial Differential Equations, by John C. Strikwerda
3. Chebyshev and Fourier Spectral Methods, by J. P. Boyd
4. Numerical Methods for Conservation Laws, by Randall J. LeVeque

Evaluation: The final grade will be computed from regular assignments (60%) and a final exam (40%).  The final exam is scheduled for Monday, December 10, 2018 from 7:45am-9:45am.