Numerical Analysis of Time Dependent Problems

Announcements: HW4 now due 6/2.

Moodle page for homework submission

Moodle discussion forum

Homework assignments (also corrections, hints, ...)

Additional reading, references, handouts, slides from lectures, etc.

Final Project

Course Description

Prerequisites

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)

• Handouts

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