AMATH 586

Numerical Analysis of Time Dependent Problems

SLN 10223, MWF 2:30-3:20, Loew Hall 216

Instructor:

Professor Randall J. LeVeque
Guggenheim 408A
tel: 685-3037
fax: 685-1440
rjl AT uw DOT edu
office hours: T,Th 9-10am

TA:

Jonathan Claridge
office hours: See Catalyst web page

Course Description

Numerical methods for time-dependent differential equations. One-step, multi-step methods. Stiff equations, implicit methods. Hyperbolic and parabolic equations. Stability and convergence theory.

Prerequisites

AMath 581 or AMath 584

Catalyst webpage

Registered class members can access the Catalyst web page to find homework assignments, the homework dropbox, and the discussion board.

Syllabus

The main topic is finite difference methods for time-dependent differential equations.

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

Textbook

Finite Difference Methods for Ordinary and Partial Differential Equations by R.J. LeVeque. (SIAM, 2007)
It will be available in the bookstore, but note that members of SIAM receive a 30% discount if you buy it online, and all UW students are eligible for free membership in SIAM, see
- Membership page
- Order book
- Book webpage (includes some m-files and exercises)

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.

Grading

Homework: 50%, midterm exam: 25%, final project: 25%. There will probably be 4 homework assignments.