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

Randall J. LeVeque

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.



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.


 

Exercises and m-files to accompany the text
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