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Symplectic effective order methods

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Abstract

A family of three stage symplectic Runge–Kutta methods are derived with effective order 4. The methods are constrained so that the coefficient matrix A has only real eigenvalues. This restriction enables transformations to be introduced into the implementation of the method so that, for large Hamiltonian problems, there is a significant gain in efficiency.

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Authors and Affiliations

  1. Department of Mathematics, University of Auckland, 1142, Auckland, New Zealand

    John C. Butcher & Gulshad Imran

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  1. John C. Butcher
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  2. Gulshad Imran
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Correspondence to John C. Butcher.

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Butcher, J.C., Imran, G. Symplectic effective order methods. Numer Algor 65, 499–517 (2014). https://doi.org/10.1007/s11075-013-9789-5

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  • DOI: https://doi.org/10.1007/s11075-013-9789-5

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