AMATH 586
SLN 1218, MWF 2:30-3:20, Mechanical Engineering Building 246
Numerical Analysis of Time Dependent Problems
Instructor:
|
Professor
Randall J. LeVeque
Guggenheim 408A
tel: 685-3037
fax: 685-1440
rjl@amath.washington.edu
office hours: T 1:30-2:30, W 9:00-10:00, Th 11:00-12:00
|
Course Description
Finite-difference methods for time-dependent differential equations.
Multistep methods, stiff equations, implicit methods.
Hyperbolic and parabolic partial differential equations.
Stability and convergence theory.
Prerequisites
AMath 581 or AMATH 584
Syllabus
The main topic is finite difference methods for time-dependent differential
equations.
- Review of 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
- Software
- 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
- Finite volume methods
- Introduction to shock capturing methods, flux limiters
- Spectral and pseudospectral methods
- Compact difference schemes
- Convection-diffusion and reaction-diffusion equations
Textbook
Other references:
- 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.
Assignments
Follow links in the table below to obtain a copy of the homework in
PostScript (.ps) or 
Adobe
Acrobat (.pdf) format. You may also obtain here solutions to some of the
homework and exam problems. An item shown below in plain text is not yet
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homework and solution sets,
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Tentative Schedule
| |
Date |
Event |
Homework Problem Sets |
| Week 1 |
M, March 29 |
First day of classes |
| Week 3 |
W, April 14 |
Homework 1 due |
hw1 |
| Week 5 |
W, April 28 |
Homework 2 due |
hw2 |
| Week 7 |
F, May 14 |
Homework 3 due |
hw3 |
| Week 8 |
W, May 19 |
Midterm |
| Week 9 |
W, May 26 |
Class until 3:45 |
| Week 9 |
F, May 28 |
Homework 4 due |
hw4 |
| Week 10 |
M, May 31 |
Memorial Day |
| Week 10 |
W, June 2 |
Class until 3:45 |
| Week 10 |
F, June 4 |
No class |
| Week 11 |
W, June 9 |
Final project due |
project |
Grading
Homework: 50%, midterm exam: 25%, final project: 25%. There will probably be 4
homework assignments.
You may view your homework and exam
grades on-line.
Before doing so for the first time, you must
request a password.
Tutorials
No on-line tutorials have been assigned for AMATH 586.