Repositorio Zaguan - Universidad de Zaragoza 

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000003263 001__ 3263
000003263 037__ $$aART--2009-001
000003263 041__ $$aeng
000003263 100__ $$aCalvo, M.$$bcalvo@unizar.es
000003263 245__ $$aOn explicit multi-revolution Runge–Kutta schemes 
000003263 260__ $$c2007-01-01
000003263 300__ $$amult. p
000003263 520__ $$aIn this paper, by using the theory of Butcher series, a general expression of the order conditions on the coefficients of a multi-revolution Runge–Kutta method is derived. A complete study of explicit multi-revolution Runge–Kutta methods of order four with four stages is given. Also, by using suitable simplifying assumptions, a family of six stage explicit methods with order five is derived and a particular method of this family (which generalizes the well known formula of order five in DOPRI5(4)) is selected by minimizing a norm of the leading term of the local truncation error. Finally, some numerical experiments are presented to test the behaviour of the new fifth-order method.
000003263 6531_ $$ainitial value problems with almost periodic or highly oscillatory solutions
000003263 6531_ $$aRunge–Kutta methods
000003263 6531_ $$along term integration
000003263 6531_ $$amulti-revolution methods
000003263 700__ $$aMontijano, Juan I.$$bmonti@unizar.es
000003263 700__ $$aRández, Luis$$brandez@unizar.es
000003263 773__ $$gVol. 26, Num. 1-3 (Enero 2007)$$pAdv. Comput. Math. $$tAdvances in Computational Mathematics$$x1572-9044
000003263 8560_ $$fmiguelm@unizar.es
000003263 8564_ $$uhttp://dx.doi.org/10.1007/s10444-004-7209-z$$zTexto completo
000003263 909CO $$ooai:zaguan.unizar.es:3263$$pdriver
000003263 9102_ $$a$$bMatemática Aplicada
000003263 980__ $$aART$$bANyA
000003263 983__ $$ainternational_article$$ainternational_article
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