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Solving Ordinary Differential Equations II

Stiff and Differential-Algebraic Problems

  • Book
  • © 1996
  • Latest edition


  • The subject of this book is the solution of stiff differential equations and of differential-algebraic systems
  • This second completely revised and enlarged edition contains, in particular, such new material as: explicit method with optimal stability, new numerical tests, properties of error growth functions, recent progress in differential-algebraic equations and improved FORTRAN codes
  • Includes supplementary material:

Part of the book series: Springer Series in Computational Mathematics (SSCM, volume 14)

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About this book

"Whatever regrets may be, we have done our best." (Sir Ernest Shack­ 0 leton, turning back on 9 January 1909 at 88 23' South.) Brahms struggled for 20 years to write his first symphony. Compared to this, the 10 years we have been working on these two volumes may even appear short. This second volume treats stiff differential equations and differential algebraic equations. It contains three chapters: Chapter IV on one-step (Runge-Kutta) meth­ ods for stiff problems, Chapter V on multistep methods for stiff problems, and Chapter VI on singular perturbation and differential-algebraic equations. Each chapter is divided into sections. Usually the first sections of a chapter are of an introductory nature, explain numerical phenomena and exhibit numerical results. Investigations of a more theoretical nature are presented in the later sections of each chapter. As in Volume I, the formulas, theorems, tables and figures are numbered con­ secutively in each section and indicate, in addition, the section number. In cross references to other chapters the (latin) chapter number is put first. References to the bibliography are again by "author" plus "year" in parentheses. The bibliography again contains only those papers which are discussed in the text and is in no way meant to be complete.

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Table of contents (38 chapters)

  1. Stiff Problems — One-Step Methods

  2. Multistep Methods for Stiff Problems


From the reviews of the second edition:

This is a superb book...Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text." Mathematics Today

“This volume, on nonstiff equations, is the second of a two-volume set. This second volume treats stiff differential equations and differential-algebraic equations. … This book is highly recommended as a text for courses in numerical methods for ordinary differential equations and as a reference for the worker. It should be in every library, both academic and industrial.” (Teodora-Liliana Rădulescu, Zentralblatt MATH, Vol. 1192, 2010)

Authors and Affiliations

  • Section de Mathématiques, C.P. 240, Université de Genève, Genève 24, Switzerland

    Ernst Hairer, Gerhard Wanner

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