Numerical Analysis of Time Dependent Problems

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Moodle page for homework submission

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

Additional reading, references, handouts etc.

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