Introduction and a short historical overview

  • Ivan P. GavrilyukEmail author
  • Martin Hermann
  • Volodymyr L. Makarov
  • Myroslav V. Kutniv
Part of the International Series of Numerical Mathematics book series (ISNM, volume 159)


One of the important fields of application for modern computers is the numerical solution of diverse problems arising in science, engineering, industry, etc. Here, mathematical models have to be solved which describe e.g. natural phenomena, industrial processes, nonlinear vibrations, nonlinear mechanical structures or phenomena in hydrodynamics and biophysics. A lot of such mathematical models can be formulated as initial value problems (IVPs) or boundary value problems (BVPs) for systems of nonlinear ordinary differential equations (ODEs). However, it is not possible in general to determine the solution of nonlinear problems in a closed form. Therefore the exact solution must be approximated by numerical techniques.


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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  • Ivan P. Gavrilyuk
    • 1
    Email author
  • Martin Hermann
    • 2
  • Volodymyr L. Makarov
    • 3
  • Myroslav V. Kutniv
    • 4
  1. 1.Staatliche Studienakademie Thüringen Berufsakademie Eisenach(University of Cooperative Education)EisenachGermany
  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

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