**Finite Difference Methods for
Ordinary and Partial Differential Equations
Steady State and Time Dependent Problems
**

Society for Industrial and Applied Mathematics (SIAM),
Philadelphia, Softcover / ISBN 978-0-898716-29-0 xiv+339 pages July, 2007. SIAM Bookstore |

You can download a tar file containing all files described below:

Execute

tar -zxvf fdmbook.tar.gz

on a Unix or Linux system to unpack. This will create a directory fdmbook with subdirectories latex, exercises, matlab.

Still under construction -- more will appear in the future

m-files can be found under on the Chapter pages below or in the matlab subdirectory.

All the exercises (including a table of contents with brief descriptions): exercises/allexercises.pdf ... exercises/allexercises.tex

A pdf file of exercises for each chapter is available on the corresponding Chapter page below.

The latex files for the exercises are also available in the exercises subdirectory, one for each exercise. These may be useful to instructors in putting together a custom set of exercises to distribute and/or to produce modified problems. They may also be useful to students who wish to write up their solutions in latex. I encourage this since it teaches students a valuable skill and makes homework much more pleasant to grade.

A sample homework assignment from AMath 586 at the University of Washington shows how these latex files can be assembled into a custom homework assignment: am586hw1.pdf ... am586hw1.tex

To use the exercise latex files, you may need some or all of the macros found in latex/macros.tex and exercises/exermacros.tex.

Sample homework and latex files are available to help students get started using latex.

**Part I: Boundary Value Problems and Iterative Methods**

**Chapter 1**
Finite difference approximations

**Chapter 2**
Steady States and Boundary Value Problems

**Chapter 3**
Elliptic Equations

**Chapter 4**
Iterative Methods for Sparse Linear Systems

**Part II: Initial Value Problems**

**Chapter 5**
The Initial Value Problem for ODEs

**Chapter 6**
Zero-Stability and Convergence for Initial Value Problems

**Chapter 7**
Absolute Stability for ODEs

**Chapter 8**
Stiff ODEs

**Chapter 9**
Diffusion Equations and Parabolic Problems

**Chapter 10**
Advection Equations and Hyperbolic Systems

**Chapter 11**
Mixed Equations

**Part III: Appendices **

**Chapter 12**
Measuring Errors

**Chapter 13**
Polynomial Interpolation and Orthogonal Polynomials

**Chapter 14**
Eigenvalues and inner product norms

**Chapter 15**
Matrix powers and exponentials

**Chapter 16**
Partial Differential Equations