This is the second edition of a book published in 1995 (Zbl 0840.65126) by the first named author. In addition to the co-author named, it should be stated that various sections of the book have been contributed by about a score of the other persons who are named in the preface. Brief biographies of the contributors and authors are given at the end of the book. It is a revised and extended (over 40%) version of the previous book and contains references to new work on the subject in the last five years. Some of the book overlaps a book edited by the first named author [Advances in computational electrodynamics: the finite-difference time-domain method, Boston, Artech House (1998; Zbl 0903.65098)]. As a result, it is impossible to give a general review of this book and the best thing is to give an indication of the new work which has been introduced.
The subjects which have received most attention are perfectly matched layer absorbing boundary conditions (there are nearly 50 new references) where J.-P. Berenger’s seminal work of 1994 [J. Comput. Phys. 114, 185-200 (1994; Zbl 0814.65129)] and its consequences are discussed and micro optical resonators where the consequences of recent advances in nano fabrication techniques allow the consideration of the practicality of microcavities. Other topics which have received substantial consideration are the modelling of antennas and the analysis of periodic structures.
New interesting topics covered are complex wave number and frequency theory, the relation of SPICE circuit models with the FDTD space lattice and discussions of algorithms involving 3D numerical stability.
Once again, the book is enhanced by figures giving the results of calculations using the methods described and a number of colour plates, and the printing and exposition are good. Attached to the book is a CD ROM written in MATLAB with sample FDTD codes and images of all of the figures and tables in the book. One is glad to note that the increase in the cost of this book is proportionally less than its increase in size. Once again, the book can be recommended, even though there is a disclaimer for errors in it by editors, authors and publishers at the beginning.