Assignment for the first week of Math 545
Explore this website. Find out about the text,
coverage, and requirements of this course.
Obtain a copy of the text
Finite Difference Methods for Ordinary and Partial
Differential Equations, by Randall J. LeVeque, SIAM,
Philadelphia, 2007. Read Chapter 5, which is mostly review.
As you are reading, please refer back to the following tips and
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- Be aware that this book uses some different notation from what
you may have seen before. For example, the symbol k is used instead
of h for the time step.
- Read carefully the discussion of local truncation error
in Sections 5.4 and 5.5. LeVeque's definition is probably different
from what you have seen before, differing by one power of k.
- The word stable has several different meanings
in numerical analysis. In Sections 5.4 and 5.5 LeVeque uses the term
stability in a way that was defined in Part I of the book.
Don't worry about this; we will discuss it in class at some point.
(We are skipping over Part I, which is material that is
covered in Math 546.)
- Pay careful attention to the material on Lipschitz continuity in
- Look over the material on the various numerical methods in
Sections 5.6 through 5.9, but don't worry about every detail. I do
recommend that you read Section 5.7.1 closely. This contains
interesting and important information that you might not have seen in
your previous course. (I did not cover it in Math 448/548.)
- Be ready to hit the decks running on Tuesday, August 30th. After
some preliminary overview material, I will begin with Section 5.9.