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Conserved Forms of Second Order-Ordinary Differential Equations

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Nonlinear Science and Complexity

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Abstract

In this paper we prove that λ-symmetries of any second-order ordinary differential equation can be used to construct an integrating factor of the equation, and that the associated conserved form can be derived from the algorithm of reduction associated to the λ-symmetry.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Cádiz, 11510 Puerto Real, Cádiz, Spain

    C. Muriel & J. L. Romero

Authors
  1. C. Muriel
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  2. J. L. Romero
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Corresponding author

Correspondence to C. Muriel .

Editor information

Editors and Affiliations

  1. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    J.A. Tenreiro Machado

  2. Dept. of Mech. & Industr. Engineering, Southern Illinois Univ. Edwardsville, Edwardsville, 62026-1805, Illinois, USA

    Albert C.J. Luo

  3. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    Ramiro S. Barbosa

  4. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    Manuel F. Silva

  5. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    Lino B. Figueiredo

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Muriel, C., Romero, J.L. (2011). Conserved Forms of Second Order-Ordinary Differential Equations. In: Machado, J., Luo, A., Barbosa, R., Silva, M., Figueiredo, L. (eds) Nonlinear Science and Complexity. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9884-9_9

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  • DOI: https://doi.org/10.1007/978-90-481-9884-9_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9883-2

  • Online ISBN: 978-90-481-9884-9

  • eBook Packages: EngineeringEngineering (R0)

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