71109 20200113145616.0 doi 10.1007/s11075-017-0374-1 sideral 100833 ART-2018-100833 eng (orcid)0000-0002-6086-9731 Franco, J.M. Universidad de Zaragoza An eighth-order exponentially fitted two-step hybrid method of explicit type for solving orbital and oscillatory problems 2018 Access copy available to the general public Unrestricted The construction of an eighth-order exponentially fitted (EF) two-step hybrid method for the numerical integration of oscillatory second-order initial value problems (IVPs) is considered. The EF two-step hybrid methods integrate exactly differential systems whose solutions can be expressed as linear combinations of exponential or trigonometric functions and have variable coefficients depending on the frequency of each problem. Based on the order conditions and the EF conditions for this class of methods, we construct an explicit EF two-step hybrid method with symmetric nodes and algebraic order eight which only uses seven function evaluations per step. This new method has the highest algebraic order we know for the case of explicit EF two-step hybrid methods. The numerical experiments carried out with several orbital and oscillatory problems show that the new eighth-order EF scheme is more efficient than other standard and EF two-step hybrid codes recently proposed in the scientific literature. info:eu-repo/grantAgreement/ES/MICINN/MTM2013-47318-C2-1-P info:eu-repo/semantics/openAccess All rights reserved http://www.europeana.eu/rights/rr-f/ 2.417 2018 MATHEMATICS, APPLIED 24 / 254 = 0.094 2018 Q1 T1 0.937 2018 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 78, 1 (2018), 243-262 Numer. algorithms Numerical Algorithms 1017-1398 216484 http://zaguan.unizar.es/record/71109/files/texto_completo.pdf Postprint 83097 http://zaguan.unizar.es/record/71109/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:71109 articulos driver 2020-01-13-14:53:22 ARTICLE