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Numerical solution of initial-value problems in differential-algebraic equations. Unabridged, corr. republ. (English) Zbl 0844.65058
Classics in Applied Mathematics. 14. Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. x, 256 p. (1996).
Differential algebraic equations (DAEs), i.e. ordinary differential equations coupled with algebraic constraints, have become widely used in applied science and the numerical solution of DAEs has been a field with much development within the last decade.
This corrected republication of the 1989 edition (Zbl 0699.65057) attempts to give the reader an understanding of many of the different aspects of solving DAEs numerically. This is done remarkably well in little over 200 pages and due to the extensive list of references (more than 150 have been added to the new edition) this monograph is an excellent gateway to the world of DAEs.
In addition to the first edition a chapter on the development since 1989 has been included. It initially contains a review of some of the theoretical advances – particularly for fully implicit nonlinear systems. Then it briefly describes some numerical advances in particular for Runge-Kutta methods.
The development in software is also summarized. Especially the use of symbolic software and automatic differentiation as well as graph theoretical algorithms have made it easier to solve DAEs. Finally, the developments in DASSL (the popular code written by one of the authors) are described – a version for large systems of DAEs as well as two new codes for sensitivity analysis have been made available.
In conclusion this book is highly recommended no matter whether one is a novice or an expert in the field or one just wishes to use the code DASSL.

65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
34A09 Implicit ordinary differential equations, differential-algebraic equations
65-02 Research exposition (monographs, survey articles) pertaining to numerical analysis
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations