Numerical Solution of Differential Equations
Math 686-001 (Spring 2024)
This web page will be updated regularly and always contain the latest information on the course.
| Instructor: | Thomas Wanner |
| Office: | Exploratory Hall 4404 |
| E-mail: | twanner@gmu.edu |
| Web Page: | https://math.cos.gmu.edu/~wanner |
| Fax: | (703) 993-1491 |
| Office hours: | TR 4-5pm, and by appointment |
| Lectures: | TR 5:55-7:10pm, Exploratory Hall 4106 |
| Prerequisites: | Math 446 or Math 685 and an elementary differential equations course. |
| Textbook: | There is no required textbook for the course, I will post handwritten lecture notes on Blackboard after every class. |
| While I will draw the material from a variety of sources, the following two texts can be used for supplementary reading: | |
| 📕 Arieh Iserles: A First Course in the Numerical Analysis of Differential Equations (2nd edition), Cambridge University Press, 2009. | |
| 📘 Evelyn Sander, Thomas Wanner: Theory and Numerics of Partial Differential Equations, Book Manuscript, in preparation, 2024. | |
| (The latest pdf version of the book manuscript will be provided.) |
Important Links
- Detailed syllabus (including notes and recommended books)
- Relevant official GMU policies
Syllabus
This course covers fundamental numerical methods for solving ordinary and partial differential equations. Specific topics include Runge-Kutta and multistep methods for ordinary differential equations, finite difference methods for initial value problems, boundary value problems, the Poisson equation, the diffusion equation, and hyperbolic equations. A more detailed syllabus can be found here. It will be updated weekly.
Homework Assignments
Homework problems will be assigned once a week and posted on Gradescope. Some of these assignments will be graded and count towards your homework score. While the remaining ones do not have to be handed in, I do advise everyone strongly to study them and write out the solutions properly. I will go through many of the homework problems in the following class and you will not benefit from this if you have not made a serious attempt at solving them.
Matlab
The software package Matlab will be used throughout the course. The university has a site license, so every student can download and use Matlab on their own computer. In addition, Matlab is available on campus computer labs, and via remote access. Matlab is a computing environment with programming capability, good graphics, and powerful library functions. Further information on Matlab can be found here.
Grading Policy
Your final grade in the course will be determined from your performance in the assigned homework, a numerical project, a class presentation, and your attendance and participation in class. Weights for these items will be distributed approximately according to the following schedule:
| Homework | Numerical Project | Presentation | Attendance |
|---|---|---|---|
| 50% | 20% | 20% | 10% |
These percentages might change, and any changes will be announced in class.