Finite Difference Methods for
Ordinary and Partial Differential Equations
Steady State and Time Dependent Problems
Randall J. LeVeque
Society for Industrial and Applied Mathematics (SIAM),
Softcover / ISBN 978-0-898716-29-0
You can download a tar file containing all files described below:
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