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"A study of the art and science of solving elliptic problems numerically, with an emphasis on problems that have important scientific and engineering applications, and that are solvable at moderate cost on computing machines."

"A concise survey of the current state of knowledge in 1972 about solving elliptic boundary-value eigenvalue problems with the help of a computer. This volume provides a case study in scientific computing -- the art of utilizing physical intuition, mathematical theorems and algorithms, and modern computer technology to construct and explore realistic models of problems arising in the natural sciences and engineering."

"Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems."

"Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. Examples drawn from a variety of applications are used to motivate and illustrate the concepts and techniques. This classic edition, originally published in 1989, is the only general DAE book available. It not only develops guidelines for choosing different numerical methods, it is the first book to discuss DAE codes, including the popular DASSL code. An extensive discussion of backward differentiation formulas details why they have emerged as the most popular and best understood class of linear multistep methods for general DAE's. New to this edition is a chapter that brings the discussion of DAE software up to date. The objective of this monograph is to advance and consolidate the existing research results for the numerical solution of DAE's. The authors present results on the analysis of numerical methods, and also show how these results are relevant for the solution of problems from applications. They develop guidelines for problem formulation and effective use of the available mathematical software and provide extensive references for further study."

"This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner."

"The Finite Element Method for Elliptic Problems is the only book available that analyzes in depth the mathematical foundations of the finite element method. It is a valuable reference and introduction to current research on the numerical analysis of the finite element method, as well as a working textbook for graduate courses in numerical analysis. It includes many useful figures, and there are many exercises of varying difficulty.Although nearly 25 years have passed since this book was first published, the majority of its content remains up-to-date. Chapters 1 through 6, which cover the basic error estimates for elliptic problems, are still the best available sources for material on this topic. The material covered in Chapters 7 and 8, however, has undergone considerable progress in terms of new applications of the finite element method; therefore, the author provides, in the Preface to the Classics Edition, a bibliography of recent texts that complement the classic material in these chapters."