78893 20191127155455.0 doi 10.1016/j.cam.2018.04.026 sideral 106372 ART-2018-106372 eng (orcid)0000-0002-6086-9731 Franco, J.M. Universidad de Zaragoza A class of explicit high-order exponentially-fitted two-step methods for solving oscillatory IVPs 2018 Access copy available to the general public Unrestricted The 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. info:eu-repo/grantAgreement/ES/MINECO/MTM2016-77735-C3-1-P info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 1.883 2018 MATHEMATICS, APPLIED 47 / 254 = 0.185 2018 Q1 T1 0.849 2018 Computational Mathematics 2018 Q2 Applied Mathematics 2018 Q2 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion (orcid)0000-0002-4238-3228 Rández, L. Universidad de Zaragoza 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 342 (2018), 210-224 J. comput. appl. math. Journal of Computational and Applied Mathematics 0377-0427 230242 http://zaguan.unizar.es/record/78893/files/texto_completo.pdf Postprint 77740 http://zaguan.unizar.es/record/78893/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:78893 articulos driver 2019-11-27-15:47:07 ARTICLE