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arXiv · 1203.3252

The minimal stage, energy preserving Runge-Kutta method for polynomial Hamiltonian systems is the Averaged Vector Field method

Elena Celledoni·Brynjulf Owren·Yajuan Sun
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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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Elena Celledoni, Brynjulf Owren, Yajuan Sun. 2012-03-15. The minimal stage, energy preserving Runge-Kutta method for polynomial Hamiltonian systems is the Averaged Vector Field method. https://arxiv.org/abs/1203.3252

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