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Numerical Methods for Partial Differential Equations

CS555 :: Spring 2023

About the Course

Are you interested in the numerical approximation of solutions to partial differential equations? Then this course is for you!

sparse matrix

The course covers roughly three topics: the fundamentals of finite difference approximations, an introduction to finite volume schemes, and comprehensive look at finite element methods.

The course involves several assignments (usually bi-weekly) and a final project that we develop over the semester, culminating in a presentation. There is also a strong participation grade based on handouts and other in-class tasks. The tentative grade breakdown is:

This will be finalized in the first week of class.

The course assignments and examples in class will be in Python.

Lectures

Lecture Date Topic
images/0-elliptic.png 01-18 About the course, classifying PDEs, survey of methods
images/0-advection1d.png 01-23 Finite differencing for time dependent problems
images/0-lw.png 01-25 Convergence theory, Stability
images/0-wiggles.png 01-30 Stabilty, dispersion, and dissipation

Homework

Guidelines and files

Books

Computing

We will be using Python with the libraries numpy, scipy and matplotlib for assignments. No other languages are permitted.

Python and Numpy Help

COVID and Attendance

While face coverings are not required in classrooms (current as of 01/17) we fully support your decision to wear one if you wish.

If you test positive for COVID, then you should not attend class.

If you have any cold-like symptoms or do not feel well, then you should not attend class, regardless of testing negative or positive for COVID.

In either case, your missed attendance due to illness will not impact your grade in the course and we will work with you to cover the material missed in class (via Zoom).