International Series of Numerical Mathematics

Exact and Truncated Difference Schemes for Boundary Value ODEs

Authors: Gavrilyuk, I., Hermann, M., Makarov, V., Kutniv, M.V.

  • Contains the first comprehensive and unified theory of compact finite difference methods for the numerical solution of nonlinear boundary value problems of ordinary differential equations (ODEs)
  • Detailed presentation of a class of methods which is very important for applications
  • Geared toward students and professionals with a good background in mathematics
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About this book

The book provides a comprehensive introduction to compact finite difference methods for solving boundary value ODEs with high accuracy. The corresponding theory is based on exact difference schemes (EDS) from which the implementable truncated difference schemes (TDS) are derived. The TDS are now competitive in terms of efficiency and accuracy with the well-studied numerical algorithms for the solution of initial value ODEs. Moreover, various a posteriori error estimators are presented which can be used in adaptive algorithms as important building blocks. The new class of EDS and TDS treated in this book can be considered as further developments of the results presented in the highly respected books of the Russian mathematician A. A. Samarskii. It is shown that the new Samarskii-like techniques open the horizon for the numerical treatment of more complicated problems.

The book contains exercises and the corresponding solutions enabling the use as a course text or for self-study. Researchers and students from numerical methods, engineering and other sciences will find this book provides an accessible and self-contained introduction to numerical methods for solving boundary value ODEs.

Reviews

From the reviews:

“The authors present a first unified theory of finite difference methods for the solution of linear and nonlinear boundary value problems (BVPs) of ordinary differential equations (ODEs). … The book is addressed to graduate students of mathematics and physics, as well as to working scientists and engineers as a self-study tool and reference. Researchers working with BVBs will find appropriate and effective numerical algorithms for their needs. … also be used as a textbook for a one- or-two- semester course on numerical methods for ODEs.” (Răzvan Răducanu, Zentralblatt MATH, Vol. 1226, 2012)


Table of contents (6 chapters)

  • Introduction and a short historical overview

    Gavrilyuk, Ivan P. (et al.)

    Pages 1-39

  • Two-point difference schemes for systems of nonlinear BVPs

    Gavrilyuk, Ivan P. (et al.)

    Pages 41-81

  • Three-point difference schemes for monotone second-order ODEs

    Gavrilyuk, Ivan P. (et al.)

    Pages 83-119

  • Three-point difference schemes for systems of monotone second-order ODEs

    Gavrilyuk, Ivan P. (et al.)

    Pages 121-156

  • Difference schemes for nonlinear BVPs on the half-axis

    Gavrilyuk, Ivan P. (et al.)

    Pages 157-201

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-0348-0107-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-0348-0106-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-0348-0341-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Exact and Truncated Difference Schemes for Boundary Value ODEs
Authors
Series Title
International Series of Numerical Mathematics
Series Volume
159
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-0107-2
DOI
10.1007/978-3-0348-0107-2
Hardcover ISBN
978-3-0348-0106-5
Softcover ISBN
978-3-0348-0341-0
Series ISSN
0373-3149
Edition Number
1
Number of Pages
XII, 248
Topics