000069435 001__ 69435 000069435 005__ 20230126102833.0 000069435 0247_ $$2doi$$a10.1007/s10444-014-9355-2 000069435 0248_ $$2sideral$$a104445 000069435 037__ $$aART-2015-104445 000069435 041__ $$aeng 000069435 100__ $$0(orcid)0000-0002-3312-5710$$aCalvo, Manuel$$uUniversidad de Zaragoza 000069435 245__ $$aRunge-Kutta projection methods with low dispersion and dissipation errors 000069435 260__ $$c2015 000069435 5060_ $$aAccess copy available to the general public$$fUnrestricted 000069435 5203_ $$aIn this paper new one-step methods that combine Runge–Kutta (RK) formulae with a suitable projection after the step are proposed for the numerical solution of Initial Value Problems. The aim of this projection is to preserve some first integral in the numerical integration. In contrast with standard orthogonal projection, the direction of the projection at each step is obtained from another suitable embed- ded formula so that the overall method is affine invariant. A study of the local errors of these projection methods is carried out, showing that by choosing proper embedded formulae the order can be increased for the harmonic oscillator. Particular embedded formulae for the third order method by Bogacki and Shampine (BS3) are provided. Some criteria to get appropriate dynamical directions for general problems as well as sufficient conditions that ensure the existence of RK methods embedded in BS3 according to them are given. Finally, some numerical experiments to test the behaviour of the new projection methods are presented. 000069435 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/MTM2010-21630-C02-01 000069435 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000069435 590__ $$a1.325$$b2015 000069435 591__ $$aMATHEMATICS, APPLIED$$b56 / 254 = 0.22$$c2015$$dQ1$$eT1 000069435 592__ $$a1.007$$b2015 000069435 593__ $$aComputational Mathematics$$c2015$$dQ2 000069435 593__ $$aApplied Mathematics$$c2015$$dQ2 000069435 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000069435 700__ $$0(orcid)0000-0002-0122-8926$$aLaburta, María Pilar$$uUniversidad de Zaragoza 000069435 700__ $$0(orcid)0000-0001-6120-4427$$aMontijano, Juan Ignacio$$uUniversidad de Zaragoza 000069435 700__ $$0(orcid)0000-0002-4238-3228$$aRández, Luis$$uUniversidad de Zaragoza 000069435 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000069435 773__ $$g41, 1 (2015), 231-251$$pAdv. comput. math.$$tADVANCES IN COMPUTATIONAL MATHEMATICS$$x1019-7168 000069435 8564_ $$s339918$$uhttps://zaguan.unizar.es/record/69435/files/texto_completo.pdf$$yPostprint 000069435 8564_ $$s56199$$uhttps://zaguan.unizar.es/record/69435/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000069435 909CO $$ooai:zaguan.unizar.es:69435$$particulos$$pdriver 000069435 951__ $$a2023-01-26-09:51:35 000069435 980__ $$aARTICLE