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** 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
guidelines.

- 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
Section 5.2
- 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.