Repositorio Zaguan - Universidad de Zaragoza 

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000003277 001__ 3277
000003277 037__ $$aART--2009-009
000003277 041__ $$aeng
000003277 100__ $$aCalvo, M.$$bcalvo@unizar.es
000003277 245__ $$aApproximate preservation of quadratic invariants by explicit Runge-Kutta methods 
000003277 260__ $$c2006
000003277 300__ $$amult. p
000003277 520__ $$aThe construction of new explicit Runge{Kutta methods taking into account, not only their accuracy, but also the preservation of Quadratic Invariants (QIs) is studied. An expression of the error of conservation of a QI by a Runge{Kutta method is given, and a new six{stage for- mula with classical order four and seventh order of QI{conservation is obtained by choosing their coe±cients so that they minimize both local and conservation errors. This formula, as well as other ones derived by Aubry and Chartier [1] and some standard formulas, have been tested with several problems with quadratic and general invariants. It is shown that the new fourth{order explicit method preserves much better the qualitative properties of the °ow than standard fourth{ order methods at the price of two extra function evaluations per step. Furthermore, it is a practical and e±cient alternative to the standard implicit methods required for a complete preservation of QIs.
000003277 6531_ $$aRunge-Kutta Methods
000003277 6531_ $$aQuadratic Invariants
000003277 6531_ $$aPseudo-Symplectic Methods
000003277 700__ $$aLaburta Santamaría, María Pilar$$blaburta@unizar.es
000003277 700__ $$aMontijano, Juan I.$$bmonti@unizar.es
000003277 700__ $$aRández, Luis$$brandez@unizar.es
000003277 8560_ $$fteresa@unizar.es
000003277 8564_ $$uhttp://zaguan.unizar.es/record/3277/files/ART--2009-009.pdf$$zTexto completo
000003277 909CO $$ooai:zaguan.unizar.es:3277$$pdriver
000003277 9102_ $$a$$bMatemática Aplicada
000003277 980__ $$aART$$bANyA
000003277 983__ $$atechnical_report
000003277 984__ $$aprivate
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