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Instructor: Professor Loyce M. Adams Office: Lewis 306 Tel: 543-5077 Fax: 685-1440 Email: lma3 AT uw DOT edu Office hours: MWF 4:00-5:00 or by appt. |
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TA: Teaching Assistant: Felix Ye Office: Lewis TBA Tel: Fax: Email: yexf308 at uw dot edu Office hours: TBA |
| Homework | Grades | Other Resources |
| Catalyst Page | EDGE Video Page | Course description | Textbook | Syllabus | Objectives | Schedule |
Catalyst WEB Page for AMATH586
Your homework will be submitted via the Homework Dropbox on the class Catalyst Page. Your written homework should be typed via Latex or some typesetting program that can be converted to .pdf format. Computer programs done in Matlab may graded by running them to check the output is correct. They will also be checked for good programming and numerical analysis practices. An analysis of the code's results as requested in the assignment will be submitted via the .pdf file to the Homework Dropbox. A goal of this course is for you to learn to analyze your computer results. You should be able to access the Catalyst site with your UW netid.Registered students click here for Homework Dropbox, Discussion Boards, and Catalyst WEB page
EDGE Streaming Video WEB Page for AMATH586
The course is recorded by EDGE. You may watch the lectures by going to the link below:Click here for EDGE Streaming Video of Lectures
Course Description and Prerequisites.
Numerical methods for time-dependent differential equations. One-step, multi-step methods. Stiff equations, implicit methods. Hyperbolic and parabolic equations. Stability and convergence theory. Prerequisities are Amath 581 or Amath 584. Amath585 will be helpful.Textbook
- Finite Difference Methods for Ordinary and
Partial Differential Equations
by R.J. LeVeque. (SIAM, 2007)
We will use Chapters 1-4 and the Appendices.
It is available through the University Libraries as an Ebook. On campus students Click here.
Off-campus students Click here.
For your information, to use the University of Washington Library service for other ebooks from off-campus, paste the link of the book into the University's Proxy on the website Click here.
Some copies 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
- Textbook 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. Combridge University Press, 1996.
- J.C. Strikwerda, Finite difference schemes and partial differential equations, Wadsworth and Brooks-Cole, 1989.
Syllabus
- 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 pdes
- Hyperbolic and parabolic equations
- Explicit and implicit methods
- Lax-Richtmyer stability, von Neumann analysis
- Methods 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
Learning Objectives and Instructor Expectations
The course will be a combination of computation and theoretical analysis. The goal is to obtain an understanding of numerical methods and their implementation, as well as learning mathematical techniques for analyzing the stability and accuracy of these methods.
There will be homework assignments roughly bi-weekly that will involve MATLAB programming and written exercises. You may consult with your classmates about how to do the homework, but you should write your own code and express the answers to the written questions in your own words. Any sources you use should be referenced.
Schedule and Homework
The homework will be assigned on the Catalyst Web site.Grading
Homework: 50%, midterm: 25%, final-project: 25%. There will 5 homework assignments.
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