Numerical Analysis of Time Dependent Problems

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. (to be published by SIAM, 2007)
  
  • Book webpage (includes some m-files and exercises)
  • On-line version of manuscript (available to 586 students only)
  • Errata (Please report other errors found!)

• 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.

Tentative Schedule

Grading