This book is an extensive revision of the earlier 2nd Edition with the same title, of 1988. The book has been rewritten in, I hope, a much more didactic manner. Subjects such as discretisations or methods for solving ordinary differential equations are prepared carefully in early chapters, and assumed in later chapters, so that there is clearer focus on the methods for partial differential equations. There are many new examples, and all programs are in Fortran 90/95, which allows a much clearer programming style than earlier Fortran versions.

In the years since the 2nd Edition, much has happened in electrochemical digital simulation. Problems that ten years ago seemed insurmountable have been solved, such as the thin reaction layer formed by very fast homogeneous reactions, or sets of coupled reactions. Two-dimensional simulations are now commonplace, and with the help of unequal intervals, conformal maps and sparse matrix methods, these too can be solved within a reasonable time.

Techniques have been developed that make simulation much more ancient, so that accurate results can be achieved in a short computing time. Stable higher-order methods have been adapted to the electrochemical context. The book is accompanied by a number of example procedures and programs, all in Fortran 90/95. These have all been verified as far as possible. While some errors might remain, they are hopefully very few. I have a debt of gratitude to a number of people who have checked the manuscript or discussed problems with me. My wife Sandra polished my English style and helped with some of the mathematics, and Tom Koch Svennesen checked many of the mathematical equations. Others I have consulted for advice of various kinds are Professor Dr. Bertel Kastening, Drs. Leslaw Bieniasz, Ole Osterby, Jorg Strutwolf and Thomas Britz. I thank the various editors at Springer for their support and patience. If I have left anybody out, I apologize. As is customary to say (and true), any errors remaining in the book cannot be blamed on anybody but myself.