Three-point difference schemes for monotone second-order ODEs

  • 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)


In this chapter we consider nonlinear monotone ODEs with Dirichlet boundary conditions. Using a non-equidistant grid we construct an EDS on a three-point stencil and prove the existence and uniqueness of its solution. Moreover, on the basis of the EDS we develop an algorithm for the construction of a three-point TDS of rank \(\bar{m}\,=\,2[(m\,+\,1)/2],{\rm{where}\,{m}}\,\varepsilon\,\mathbb{N}\) is a given natural number and [·] denotes the entire part of the argument in brackets. We prove the existence and uniqueness of the solution of the TDS and determine the order of accuracy. Numerical examples are given which confirm the theoretical results.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations