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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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The minimal stage, energy preserving Runge–Kutta method for polynomial Hamiltonian systems is the averaged vector field method
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by Elena Celledoni, Brynjulf Owren and Yajuan Sun PDF
Math. Comp. 83 (2014), 1689-1700 Request permission

Abstract:

No Runge–Kutta method can be energy preserving for all Hamiltonian systems. But for problems in which the Hamiltonian is a polynomial, the averaged vector field (AVF) method can be interpreted as a Runge–Kutta method whose weights $b_i$ and abscissae $c_i$ represent a quadrature rule of degree at least that of the Hamiltonian. We prove that when the number of stages is minimal, the Runge–Kutta scheme must in fact be identical to the AVF scheme.
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Additional Information
  • Elena Celledoni
  • Affiliation: Department of Mathematical Sciences, NTNU, N-7491 Trondheim, Norway
  • MR Author ID: 623033
  • Email: elenac@math.ntnu.no
  • Brynjulf Owren
  • Affiliation: Department of Mathematical Sciences, NTNU, N-7491 Trondheim, Norway
  • MR Author ID: 292686
  • Email: bryn@math.ntnu.no
  • Yajuan Sun
  • Affiliation: LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences (CAS), P.O. Box 2719, Beijing 100190, China
  • Email: sunyj@lsec.cc.ac.cn
  • Received by editor(s): November 5, 2012
  • Published electronically: January 24, 2014
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 83 (2014), 1689-1700
  • MSC (2010): Primary 65P10, 65L05; Secondary 65L06, 37M99
  • DOI: https://doi.org/10.1090/S0025-5718-2014-02805-6
  • MathSciNet review: 3194126