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Integration of ODE with a small parameter via approximate symmetries: reduction of approximate symmetry algebra to a canonical form
Responsible organisation
May 27 (English)Conference paper, Presentation (Refereed) Published
Abstract [en]

The simplest method of integration of second-order differential equations using the Lie's canonical forms of two-dimensional algebras is well-known. We propose a generalization of this method on a case of integration of second-order differential equation with a small parameter having two approximate symmetries. The solution of such problem is reduced to the followings: 1) to classify approximate Lie algebras with two essential operators. As a result, seven different types of such Lie algebras have been obtained; 2) to construct canonical form of basic operators of non-similar algebras of every types for their realization in R2; 3) to set up general forms of invariant equations and formulas of their approximate solutions. The similar problems are solved for systems of two ordinary differential equations with two approximate symmetries. On this way we have constructed representation of non-similar approximated Lie algebras in R3.

Place, publisher, year, edition, pages
Karlskrona, Sweden, May 27.
Keyword [en]
Approximate symmetries, invariant equations, integration of second-order differential equation with a small parameter
National Category
Mathematics
Identifiers
URN: urn:nbn:se:bth-8708Local ID: oai:bth.se:forskinfo064DFE8D4B08FEB0C12573C9003D3128OAI: oai:DiVA.org:bth-8708DiVA: diva2:836459
Conference
International conference MOGRAN 11
Available from: 2012-09-18 Created: 2008-01-07 Last updated: 2015-06-30Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
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  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
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