SLN 10220, MWF 2:30-3:20, Condon 109
Numerical Analysis of Time Dependent Problems
Randall J. LeVeque
Condon Hall 732
office hours: MW 3:30-4:30, F 9-10, or drop by / make appt
Finite-difference methods for time-dependent differential equations.
Multistep methods, stiff equations, implicit methods.
Hyperbolic and parabolic partial differential equations.
Stability and convergence theory.
AMath 581 or AMath 584
The main topic is finite difference methods for time-dependent differential
- Numerical methods for ODEs (initial value problems)
- Consistency, convergence
- Zero stability and absolute stability, stability regions
- Linear multistep and Runge-Kutta methods
- Stiff problems, BDF methods
- Choice of method
- Numerical Methods for time-dependent partial differential equations
- Hyperbolic and parabolic equations
- Explicit and implicit methods
- Lax-Richtmyer stability, von Neumann analysis
- Method of lines approach, relation to stiff ODEs
- Introduction to finite volume methods, shock capturing methods
- High order methods
- Mixed equations, e.g., advection-reaction-diffusion equations
- Finite Difference Methods for Ordinary and
Partial Differential Equations
by R.J. LeVeque. (to be published by SIAM, 2007)
- J. D. Lambert, Numerical methods for ordinary differential systems:
the initial value problem, Wiley, 1991.
- A. Iserles. Numerical Analysis of Differential Equations.
Cambridge University Press, 1996.
- J. C. Strikwerda, Finite difference schemes and partial
differential equations, Wadsworth & Brooks/Cole, 1989.
| Week 1
||M, March 26
||First day of classes
||F, March 30
| Week 2
||F, April 6
||Homework 1 due
| Week 4
||F, April 20
||Homework 2 due
| Week 7
||M, May 7
||Homework 3 due
||F, May 11
| Week 9
||F, May 25
| Week 10
||M, May 28
||W, May 30
||Homework 4 due
| Week 10
||F, June 1
| Week 11
||W, June 6
||Final project due
Homework: 50%, midterm exam: 25%, final project: 25%. There will probably be 4