Scientific Computing with Ordinary Differential Equations

1. Front Matter

   Pages i-xix

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2. Time-Dependent Processes in Science and Engineering

   • Peter Deuflhard, Folkmar Bornemann

   Pages 1-31

3. Existence and Uniqueness for Initial Value Problems

   • Peter Deuflhard, Folkmar Bornemann

   Pages 33-73

4. Condition of Initial Value Problems

   • Peter Deuflhard, Folkmar Bornemann

   Pages 75-119

5. One-Step Methods for Nonstiff IVPs

   • Peter Deuflhard, Folkmar Bornemann

   Pages 121-190

6. Adaptive Control of One-Step Methods

   • Peter Deuflhard, Folkmar Bornemann

   Pages 191-218

7. One-Step Methods for Stiff ODE and DAE IVPs

   • Peter Deuflhard, Folkmar Bornemann

   Pages 219-311

8. Multistep Methods for ODE and DAE IVPs

   • Peter Deuflhard, Folkmar Bornemann

   Pages 313-387

9. Boundary Value Problems for ODEs

   • Peter Deuflhard, Folkmar Bornemann

   Pages 389-460

10. Back Matter

    Pages 461-486

    PDF

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in re­ search and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numeri­ cal and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mathe­ matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.

• BVP
• Boundary value problem
• calculus
• numerical analysis
• ordinary differential equation
• ordinary differential equations
• scientific computing

P. Deuflhard and F. Bornemann

Scientific Computing with Ordinary Differential Equations

"Provides a sound fundamental introduction to the mathematical and numerical aspects of discretization methods for solving initial value problems in ordinary differential equations . . . This book would make an interesting (non-conventional) textbook for a graduate course in numerical analysis of ODEs. It is written at a level which is accessible to such an audience, covers a wide variety of topics, both classical and modern, and contains a generous supply of homework exercises. In summary, this is an excellent and timely book."—MATHEMATICAL REVIEWS

"As indicated by the title, this is not a treatise merely on the numerical analysis of ordinary differential equations (ODEs). … the reader is made acquainted with nontrivial examples of ODEs arising in diverse areas and with intrinsic properties of these equations. … The consideration of all the various components … makes for a very informative reading which is further aided by the undogmatic style of presentation. The volume can be recommended to newcomers, but also to instructors in this area." (H. Muthsam, Monatshefte für Mathematik, Vol. 143 (1), 2004)

• Konrad-Zuse-Zentrum Berlin, Berlin-Dahlem, Germany

  Peter Deuflhard

• Center for Mathematical Sciences, Munich University of Technology (TUM), Munich, Germany

  Folkmar Bornemann

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