Dieter Britz – författare

This book explains how the partial differential equations (pdes) in electroanalytical chemistry can be solved numerically. It guides the reader through the topic in a very didactic way, by first introducing and discussing the basic equations along with some model systems as test cases systematically. Then it outlines basic numerical approximations for derivatives and techniques for the numerical solution of ordinary differential equations. Finally, more complicated methods for approaching the pdes are derived.The authors describe major implicit methods in detail and show how to handle homogeneous chemical reactions, even including coupled and nonlinear cases. On this basis, more advanced techniques are briefly sketched and some of the commercially available programs are discussed. In this way the reader is systematically guided and can learn the tools for approaching his own electrochemical simulation problems. This new fourth edition has been carefully revised, updated and extended compared to the previous edition (Lecture Notes in Physics Vol. 666). It contains new material describing migration effects, as well as arrays of ultramicroelectrodes. It is thus the most comprehensive and didactic introduction to the topic of electrochemical simulation.

This book explains how the partial differential equations (pdes) in electroanalytical chemistry can be solved numerically. It guides the reader through the topic in a very didactic way, by first introducing and discussing the basic equations along with some model systems as test cases systematically. Then it outlines basic numerical approximations for derivatives and techniques for the numerical solution of ordinary differential equations. Finally, more complicated methods for approaching the pdes are derived.The authors describe major implicit methods in detail and show how to handle homogeneous chemical reactions, even including coupled and nonlinear cases. On this basis, more advanced techniques are briefly sketched and some of the commercially available programs are discussed. In this way the reader is systematically guided and can learn the tools for approaching his own electrochemical simulation problems. This new fourth edition has been carefully revised, updated and extended compared to the previous edition (Lecture Notes in Physics Vol. 666). It contains new material describing migration effects, as well as arrays of ultramicroelectrodes. It is thus the most comprehensive and didactic introduction to the topic of electrochemical simulation.

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 did- tic manner. Subjects such as discretisations or methods for solving ordinary di?erential equations are prepared carefully in early chapters, and assumed in later chapters, so that there is clearer focus on the methods for partial di?erential equations. There are many new examples, and all programs are inFortran90/95,whichallows amuchclearerprogrammingstylethanearlier 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 e?cient, 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 (on the webpage www.springerlink.com/ openurl.asp?genre=issue&issn=1616-6361&volume=666) by a number of - ample procedures and programs, all in Fortran 90/95. These have all been veri?edasfaraspossible.Whilesomeerrorsmightremain,theyarehopefully very few.

This book is an extensive revision of the earlier book with the same title, 1981. The reader who has the first edition will recognise chapters 1-3 and parts of Chapt. 4; thereafter, there is little similarity. There are several reasons for this. Firstly, as one internal Danish publication stated, the first edition contained "et hav af smafejl" meaning (with some poetic license), a sea of troubles. I welcomed the opportunity of setting this right. Secondly, a number of readers rightly criticised my glib dismissal of problems connected with homogeneous chemical reactions in the first edition, now dealt with. Thirdly, digital simulation has not stood still since 1980 and this book reflects the newer developments such as orthogonal collocation, algorithms for the implicit boundary value calculations, as well as my own recent findings. Despite all this activity, no text has appeared to displace that of Feldberg (1969) or my first edition of 1981. My aim is to explain the subject clearly and simply. The electrochemist (or student) who occasionally needs to simulate a diffusion problem numerically but does not wish to go in for sophisticated methods, can make do with the first four chapters. Desk time is then traded for computer time. If this becomes excessive and/or the simulator''s interest in more efficient techniques is aroused, Chapt. 5 provides an introduction. The easiest of these is the Runge-Kutta integration method, providing a modest but definite gain in efficiency at very small cost in terms of desk time.