On approximate solutions to one class of nonlinear differential equations

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Abstract

We consider a class of systems of nonlinear ordinary differential equations with parameters. In particular, systems of such type arise when modeling the multistage synthesis of a substance. We study properties of solutions to the systems and propose a method for approximate solving the systems in the case of very large coefficients. We establish approximation estimates and show that the convergence rate depends on the parameters characterizing the nonlinearity of the systems. Moreover, the larger the coefficients of the systems, the more exact the approximate solutions. Thereby this method allows us to avoid difficulties arising inevitably when solving systems of nonlinear differential equations with very large coefficients.

Original languageEnglish
Title of host publicationMathematics and Computing - 3rd International Conference, ICMC 2017, Proceedings
PublisherSpringer-Verlag GmbH and Co. KG
Pages221-231
Number of pages11
ISBN (Print)9789811046414
DOIs
Publication statusPublished - 1 Jan 2017
Event3rd International Conference on Mathematics and Computing, ICMC 2017 - Haldia, India
Duration: 17 Jan 201721 Jan 2017

Publication series

NameCommunications in Computer and Information Science
Volume655
ISSN (Print)1865-0929

Conference

Conference3rd International Conference on Mathematics and Computing, ICMC 2017
CountryIndia
CityHaldia
Period17.01.201721.01.2017

Keywords

  • Cauchy problem
  • Estimates for solutions
  • Large coefficients
  • Limit theorems
  • Systems of ordinary differential equations

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