Exact and Truncated Difference Schemes for Boundary Value ODEs

  • Ivan Gavrilyuk
  • Martin Hermann
  • Volodymyr Makarov
  • Myroslav V. Kutniv

Part of the International Series of Numerical Mathematics book series (ISNM, volume 159)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Ivan P. Gavrilyuk, Martin Hermann, Volodymyr L. Makarov, Myroslav V. Kutniv
    Pages 1-39
  3. Ivan P. Gavrilyuk, Martin Hermann, Volodymyr L. Makarov, Myroslav V. Kutniv
    Pages 41-81
  4. Ivan P. Gavrilyuk, Martin Hermann, Volodymyr L. Makarov, Myroslav V. Kutniv
    Pages 83-119
  5. Ivan P. Gavrilyuk, Martin Hermann, Volodymyr L. Makarov, Myroslav V. Kutniv
    Pages 121-156
  6. Ivan P. Gavrilyuk, Martin Hermann, Volodymyr L. Makarov, Myroslav V. Kutniv
    Pages 157-201
  7. Ivan P. Gavrilyuk, Martin Hermann, Volodymyr L. Makarov, Myroslav V. Kutniv
    Pages 203-238
  8. Back Matter
    Pages 239-247

About this book

Introduction

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.

Authors and affiliations

  • Ivan Gavrilyuk
    • 1
  • Martin Hermann
    • 2
  • Volodymyr Makarov
    • 3
  • Myroslav V. Kutniv
    • 4
  1. 1.Berufsakademie Eisenach, University of CStaatliche Studienakademie ThüringenEisenachGermany
  2. 2., Institute of Applied MathematicsFriedrich Schiller UniversityJenaGermany
  3. 3., Institute of MathematicsNational Academy of Sciences of UkraineKiev-4Ukraine
  4. 4., Institute of Applied MathematicsLviv Polytechnical National UniversityLvivUkraine

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-0348-0107-2
  • Copyright Information Springer Basel AG 2011
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-0348-0106-5
  • Online ISBN 978-3-0348-0107-2
  • About this book
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