Numerical Analysis of Time Dependent Problems
SLN 10223, MWF 2:30-3:20, Loew Hall 216
Professor Randall J. LeVeque
rjl AT uw DOT edu
office hours: T,Th 9-10am
office hours: See
Catalyst web page
Numerical methods for time-dependent differential equations. One-step,
multi-step methods. Stiff equations, implicit methods. Hyperbolic and
parabolic equations. Stability and convergence theory.
AMath 581 or AMath 584
Registered class members can access the
Catalyst web page
to find homework
assignments, the homework dropbox, and the discussion board.
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. (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
- J. D. Lambert, Numerical methods for ordinary differential
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.
Homework: 50%, midterm exam: 25%, final project: 25%. There will probably be