Solving Ordinary Differential Equations I

1. Front Matter

   Pages i-xiii

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2. Classical Mathematical Theory

   • Ernst Hairer, Syvert Paul Nørsett, Gerhard Wanner

   Pages 1-125

3. Runge-Kutta and Extrapolation Methods

   • Ernst Hairer, Syvert Paul Nørsett, Gerhard Wanner

   Pages 127-301

4. Multistep Methods and General Linear Methods

   • Ernst Hairer, Syvert Paul Nørsett, Gerhard Wanner

   Pages 303-432

5. Back Matter

   Pages 433-482

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"So far as I remember, I have never seen an Author's Pre­ face which had any purpose but one - to furnish reasons for the publication of the Book. " (Mark Twain) "Gauss' dictum, "when a building is completed no one should be able to see any trace of the scaffolding," is often used by mathematicians as an excuse for neglecting the motivation behind their own work and the history of their field. For­ tunately, the opposite sentiment is gaining strength, and numerous asides in this Essay show to which side go my sympathies. " (B. B. Mandelbrot, 1982) 'This gives us a good occasion to work out most of the book until the next year. " (the Authors in a letter, dated c. kt. 29, 1980, to Springer Verlag) There are two volumes, one on non-stiff equations, now finished, the second on stiff equations, in preparation. The first volume has three chapters, one on classical mathematical theory, one on Runge­ Kutta and extrapolation methods, and one on multistep methods. There is an Appendix containing some Fortran codes which we have written for our numerical examples. Each chapter is divided into sections. Numbers of formulas, theorems, tables and figures are consecutive in each section and indi­ cate, in addition, the section number, but not the chapter number. Cross references to other chapters are rare and are stated explicitly. The end of a proof is denoted by "QED" (quod erat demonstrandum).

• Gewöhnliche Differentialgleichungen
• Mehrschrittverfahren
• Multistep Methods
• Numerical Analysis
• Numerische Analysis
• Ordinary Differential Equations
• Runge-Kutta-Methoden
• Runge-Kutta-Methods
• differential equation
• ordinary differential equation

From the reviews

“This is the revised version of the first edition of Vol. I published in 1987. ….Vols. I and II (SSCM 14) of Solving Ordinary Differential Equations together are the standard text on numerical methods for ODEs. ...This book is well written and is together with Vol. II, the most comprehensive modern text on numerical integration methods for ODEs. It may serve a a text book for graduate courses, ...and also as a reference book for all those who have to solve ODE problems numerically.” Zeitschrift für Angewandte Mathematik und Physik

“… This book is a valuable tool for students of mathematics and specialists concerned with numerical analysis, mathematical physics, mechanics, system engineering, and the application of computers for design and planning…” Optimization

“… 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.” Mathematics and Computers

• Section de Mathématiques, Université de Genève, Genève 24, Switzerland

  Ernst Hairer, Gerhard Wanner

• Department of Numerical Mathematics, University of Trondheim, NTH, Trondheim, Norway

  Syvert Paul Nørsett

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