Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations (Classics in Applied Mathematics)

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From the Preface:
Differential-algebraic equations (DAE's) arise naturally in many applications, but present numerical and analytical difficulties which do not occur with ordinary differential equations. The numerical solution of these types of systems has been the subject of intense research ctivity in the past few years. A great deal of progress has been male in the understanding of the mathematical struture of DAE's, the analysis of numerical methods applied to DAE systems, the development of robust and efficient mathematical software implementing the numerical methods, and the formulation and solution of DAE systems arising from problems in science and engineering. Many of the results of this research effort are scattered throughout the literature. Our objective in writing this monograph has been to bring together these developments in a unified way, making them more easily accessible to the engineers, scientists, applied mathematicians and numerical analysts who are solving DAE systems or pursuing further research in this area. We have tried not only to present the results on the analysis of numerical methods, but also to show how these results are relevant for the solution of problems from applications and to develop guidelines for problem formulation and effective use of the available mathematical software.

As in every effort of this type, time and spce constraints marie it imposible for us to aidrees in detail all of the recent research in this field. The research which we have chosen to describe is a reflection of our hope of leaving the reader with a intuitive understanding of those properties of DA! systems and their numerical solution which would in our opinion be most useful in the modeling of problems from science and engineering. In case where a more extensive description can be found in the literature, we have given references.

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