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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Numerical approximation to ODEs using the error functional
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by L. Bayón, J. M. Grau, M. M. Ruiz and P. M. Suárez PDF
Proc. Amer. Math. Soc. 140 (2012), 4295-4308 Request permission

Abstract:

In this paper we present a new method for solving systems of ordinary nonlinear differential equations with initial conditions. The method is based on the transformation of the problem to an optimal control problem. We then solve it with a technique based on the use of an integral form of the Euler equation combined with the shooting method and the cyclic coordinate descent method. Our method substantially improves a previous approach that uses iterative dynamic programming to solve the associated optimal control problem. We consider the error functional instead of the classical global error, the error functional obtained by our method being lower than that obtained by classical methods. The method presented in this paper allows us to solve a wide range of nth order ordinary nonlinear differential equations with initial conditions.
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Additional Information
  • L. Bayón
  • Affiliation: Department of Mathematics, University of Oviedo, E.P.I. Campus of Viesques, Gijón, 33203, Spain
  • Email: bayon@uniovi.es
  • J. M. Grau
  • Affiliation: Department of Mathematics, University of Oviedo, E.P.I. Campus of Viesques, Gijón, 33203, Spain
  • M. M. Ruiz
  • Affiliation: Department of Mathematics, University of Oviedo, E.P.I. Campus of Viesques, Gijón, 33203, Spain
  • P. M. Suárez
  • Affiliation: Department of Mathematics, University of Oviedo, E.P.I. Campus of Viesques, Gijón, 33203, Spain
  • Received by editor(s): December 14, 2010
  • Received by editor(s) in revised form: June 3, 2011
  • Published electronically: April 24, 2012
  • Additional Notes: This work was supported by the Government of Principality of Asturias through PCTI: FICYT IB09-085 and by the Spanish Government (MICINN, project: MTM2010-15737)
  • Communicated by: Yingfei Yi
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 4295-4308
  • MSC (2010): Primary 65L05, 47J30
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11340-1
  • MathSciNet review: 2957220