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Journal of Mathematical Sciences

, Volume 181, Issue 3, pp 383–400 | Cite as

Exact three-point difference scheme for a nonlinear boundary-value problem on the semiaxis

  • M. V. Kutniv
  • O. I. Pazdrii
Article
  • 24 Downloads

For the numerical solution of boundary-value problems on the semiaxis for second-order nonlinear ordinary differential equations, an exact three-point difference scheme is constructed and substantiated. Under the conditions of existence and uniqueness of solution of a boundary-value problem, we prove the existence and uniqueness of solution of the exact three-point difference scheme and convergence of the method of successive approximations for its solution.

Keywords

Difference Scheme Successive Approximation Contracting Mapping Nonlinear Ordinary Differential Equation Nonlinear Boundary Condition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    I. P. Gavrilyuk, M. Hermann, M. V. Kutniv, and V. L. Makarov, “Difference schemes for nonlinear BVPs on the semiaxis,” Comput. Meth. Appl. Math., 7, No. 1, 25–47 (2007).MathSciNetMATHGoogle Scholar
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    I. P. Gavrilyuk, M. Hermann, M. V. Kutniv, and V. L. Makarov, “Three-point difference schemes of variable order for nonlinear BVPs on the semiaxis,” in: Techn. Report 05–04, Friedrich Schiller University Jena, Dep. Math. Comput. Sci. (2005), pp. 1–37.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  • M. V. Kutniv
    • 1
  • O. I. Pazdrii
    • 1
  1. 1.LvivUkraine

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