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- W1979087820 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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=b Subscript i> <mml:semantics> <mml:msub> <mml:mi>b</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>b_i</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and abscissae <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=c Subscript i> <mml:semantics> <mml:msub> <mml:mi>c</mml:mi> <mml:mi>i</mml:mi> </mml:msub> <mml:annotation encoding=application/x-tex>c_i</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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." @default.
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- W1979087820 date "2014-01-24" @default.
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- W1979087820 title "The minimal stage, energy preserving Runge–Kutta method for polynomial Hamiltonian systems is the averaged vector field method" @default.
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- W1979087820 doi "https://doi.org/10.1090/s0025-5718-2014-02805-6" @default.
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