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The method of nonlocal transformations: Applications to singularly perturbed boundary-value problems

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Abstract

We present a method of numerical integration of singularly perturbed boundary-value problems with a small parameter, based on introducing a new nonlocal independent variable. As a result, we obtain more suitable problems that allow the application of standard fixed-step numerical methods. Two test boundary-value problems for second-order ODEs that have monotonic and non-monotonic exact or asymptotic solutions, expressed in elementary functions, are considered. Comparison of numerical, exact, and asymptotic solutions showed the high efficiency of the method based on generalized nonlocal transformations for solving singular boundary-value problems with a small parameter.

Original languageEnglish
Article number012047
JournalJournal of Physics: Conference Series
Volume1205
Issue number1
DOIs
StatePublished - 7 May 2019
Externally publishedYes
Event7th International Conference Problems of Mathematical Physics and Mathematical Modelling, MPMM 2018 - Moscow, Russian Federation
Duration: 25 Jun 201827 Jun 2018

Bibliographical note

Publisher Copyright:
© 2019 Published under licence by IOP Publishing Ltd.

Keywords

  • boundary layers
  • nonlinear dierential equations
  • nonlocal transformations
  • numerical and exact solutions
  • singularly perturbed boundary-value problems

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