{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:10:11Z","timestamp":1759839011533},"reference-count":15,"publisher":"American Mathematical Society (AMS)","issue":"288","license":[{"start":{"date-parts":[[2015,1,24]],"date-time":"2015-01-24T00:00:00Z","timestamp":1422057600000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>No Runge\u2013Kutta 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\u2013Kutta method whose weights <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"b Subscript i\">\n  <mml:semantics>\n    <mml:msub>\n      <mml:mi>b<\/mml:mi>\n      <mml:mi>i<\/mml:mi>\n    <\/mml:msub>\n    <mml:annotation encoding=\"application\/x-tex\">b_i<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/inline-formula> and abscissae <inline-formula content-type=\"math\/mathml\">\n<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"c Subscript i\">\n  <mml:semantics>\n    <mml:msub>\n      <mml:mi>c<\/mml:mi>\n      <mml:mi>i<\/mml:mi>\n    <\/mml:msub>\n    <mml:annotation encoding=\"application\/x-tex\">c_i<\/mml:annotation>\n  <\/mml:semantics>\n<\/mml:math>\n<\/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\u2013Kutta scheme must in fact be identical to the AVF scheme.<\/p>","DOI":"10.1090\/s0025-5718-2014-02805-6","type":"journal-article","created":{"date-parts":[[2014,1,24]],"date-time":"2014-01-24T16:48:41Z","timestamp":1390582121000},"page":"1689-1700","source":"Crossref","is-referenced-by-count":25,"title":["The minimal stage, energy preserving Runge\u2013Kutta method for polynomial Hamiltonian systems is the averaged vector field method"],"prefix":"10.1090","volume":"83","author":[{"given":"Elena","family":"Celledoni","sequence":"first","affiliation":[]},{"given":"Brynjulf","family":"Owren","sequence":"additional","affiliation":[]},{"given":"Yajuan","family":"Sun","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2014,1,24]]},"reference":[{"issue":"2","key":"1","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s002110050022","article-title":"Canonical B-series","volume":"67","author":"Calvo, M. 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