```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