Numerical Methods for Partial Differential Equations

Documents and resources

Here are some resources in PDF files.

• The text is Partial Differential Equations with Numerical Methods by Stig Larsson and Vidar Thomée; if you visit that link from a Purdue IP address you can download chapters of the book in PDF format without charge.
• A reference (especially for the multigrid method) is The Mathematical Theory of Finite Element Methods, by Susanne E. Brenner and L. Ridgway Scott. Again, accessing that link from a Purdue IP address should allow you to download the entire text.
• If you need a review of basic Real Analysis, study the books Basic Concepts of Mathematics and Mathematical Analysis I (the first four chapters).
• The previous Scheme standard. Use this to find out what is in standard Scheme; there are a lot of very general mathematics functions in Scheme, see the examples.
• The Gambit manual is available in either html or PDF format. Important parts to know are the interpreter, the compiler, the debugger, declarations, loading and including files, and homogeneous vectors.
• The Meroon manual. The first project describes the differences between Meroon as described in the manual and how it's installed here.

To learn how to program in this style, work through the first two chapters of The Structure and Interpretation of Computer Programs or use other resources to learn Scheme on my home page.

To use Gambit have /pkgs/Gambit/current/bin/ in your path. The regular Gambit interpreter and compiler are called gsi and gsc; the versions of the Gambit interpreter and compiler that have Meroon preloaded are called gsi++ and gsc++.

There are sources for various software packages. I've put together a separate software installation page with some notes about how to install them yourself if you want. (But, PLEASE, read some documentation, README files, etc., to learn a bit about it on your own.)

• Gambit web site.
• The Meroon sources.
• There is the software page for this class.
• Instructions about how to use Gambit and Meroon with mpi.

Project suggestions

I've collected some suggestions for projects. You don't need to choose a project from this list, you can choose any other project with my approval. You will need to choose a project soon after spring break. If we haven't yet covered a project on this list yet (for parabolic problems, hyperbolic problems, etc.) then look in the textbook to see what these problems are like and decide whether you'd like to work on them.

Exercises and notes

• Project -1: Learn how to use commands for your command line shell (default for math department linux servers: tcsh; default for Mac OS X: bash; default for other systems: who knows; and these can be changed). Learn how to change your path and your LD_LIBRARY_PATH. If you're on Windows use MINGW or you're on your own. Learn basic emacs commands: ^X^S to save a file, ^X^C to exit, ^-SHIFT-_ to undo, ^W to erase, select a region and TAB to indent the region, TAB to indent the current line. ("^" means hold down the control key while hitting the next key.) Become familiar with your computer as a development workstation.
• Project 0: Work through the first two chapters of SICP. Don't read the chapters, sit in front of a Gambit interpreter and work through them.
• The first draft of the first part of the first project (just to get you going with Scheme/Gambit/Meroon). The code listed in this document and the next is contained in the file project1.scm.
• The zeroth draft of the second part of the first project (lots of typos, unfortunately).