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000078893 005__ 20191127155455.0
000078893 0247_ $$2doi$$a10.1016/j.cam.2018.04.026
000078893 0248_ $$2sideral$$a106372
000078893 037__ $$aART-2018-106372
000078893 041__ $$aeng
000078893 100__ $$0(orcid)0000-0002-6086-9731$$aFranco, J.M.$$uUniversidad de Zaragoza
000078893 245__ $$aA class of explicit high-order exponentially-fitted two-step methods for solving oscillatory IVPs
000078893 260__ $$c2018
000078893 5060_ $$aAccess copy available to the general public$$fUnrestricted
000078893 5203_ $$aThe derivation of new exponentially fitted (EF) modified two-step hybrid (MTSH) methods for the numerical integration of oscillatory second-order IVPs is analyzed. These methods are modifications of classical two-step hybrid methods so that they integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions {exp(¿t), exp(-¿t)}, ¿¿C, or equivalently {sin(¿t), cos(¿t)} when ¿=i¿, ¿¿R, where ¿ represents an approximation of the main frequency of the problem. The EF conditions and the conditions for this class of EF schemes to have algebraic order p (with p=8) are derived. With the help of these conditions we construct explicit EFMTSH methods with algebraic orders seven and eight which require five and six function evaluation per step, respectively. These new EFMTSH schemes are optimal among the two-step hybrid methods in the sense that they reach a certain order of accuracy with minimal computational cost per step. In order to show the efficiency of the new high order explicit EFMTSH methods in comparison to other EF and standard two-step hybrid codes from the literature some numerical experiments with several orbital and oscillatory problems are presented.
000078893 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77735-C3-1-P
000078893 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000078893 590__ $$a1.883$$b2018
000078893 591__ $$aMATHEMATICS, APPLIED$$b47 / 254 = 0.185$$c2018$$dQ1$$eT1
000078893 592__ $$a0.849$$b2018
000078893 593__ $$aComputational Mathematics$$c2018$$dQ2
000078893 593__ $$aApplied Mathematics$$c2018$$dQ2
000078893 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000078893 700__ $$0(orcid)0000-0002-4238-3228$$aRández, L.$$uUniversidad de Zaragoza
000078893 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000078893 773__ $$g342 (2018), 210-224$$pJ. comput. appl. math.$$tJournal of Computational and Applied Mathematics$$x0377-0427
000078893 8564_ $$s230242$$uhttps://zaguan.unizar.es/record/78893/files/texto_completo.pdf$$yPostprint
000078893 8564_ $$s77740$$uhttps://zaguan.unizar.es/record/78893/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000078893 909CO $$ooai:zaguan.unizar.es:78893$$particulos$$pdriver
000078893 951__ $$a2019-11-27-15:47:07
000078893 980__ $$aARTICLE