000162226 001__ 162226 000162226 005__ 20251017144628.0 000162226 0247_ $$2doi$$a10.1016/j.apnum.2025.06.017 000162226 0248_ $$2sideral$$a144824 000162226 037__ $$aART-2025-144824 000162226 041__ $$aeng 000162226 100__ $$aHigueras, I. 000162226 245__ $$aLow-storage exponentially fitted explicit Runge-Kutta methods 000162226 260__ $$c2025 000162226 5060_ $$aAccess copy available to the general public$$fUnrestricted 000162226 5203_ $$aIn this paper, we study explicit Runge-Kutta (RK) methods for solving high-dimensional systems of ordinary differential equations (ODEs), with oscillatory or periodic solutions, that can be implemented with a few memory registers. We will refer to these schemes as Low-Storage Exponentially Fitted explicit Runge-Kutta methods (LSEFRK). In order to obtain them, we first study second-order and third-order low-storage (LS) schemes that can be implemented with two memory registers per step of the van der Houwen- and Williamson-type. Next, we construct optimal LSEFRK methods by imposing exponential fitting conditions along with accuracy and stability properties. In this way, new optimal three-stage third-order and five-stage fourth-order LSEFRK schemes are constructed for each type of LS method. The performance of these new schemes is tested by solving some high-dimensional differential systems with periodic solutions. Comparison with other non-LS exponentially fitted and low-storage non-EF RK methods from the literature shows that the new LSEFRK schemes outperform the efficiency of RK methods that only satisfy either the LS or the EF condition. 000162226 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es 000162226 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000162226 700__ $$0(orcid)0000-0001-6120-4427$$aMontijano, J.I.$$uUniversidad de Zaragoza 000162226 700__ $$0(orcid)0000-0002-4238-3228$$aRández, L.$$uUniversidad de Zaragoza 000162226 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000162226 773__ $$g217 (2025), 372-389$$pAppl. numer. math.$$tAPPLIED NUMERICAL MATHEMATICS$$x0168-9274 000162226 8564_ $$s1302330$$uhttps://zaguan.unizar.es/record/162226/files/texto_completo.pdf$$yVersión publicada 000162226 8564_ $$s1638513$$uhttps://zaguan.unizar.es/record/162226/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000162226 909CO $$ooai:zaguan.unizar.es:162226$$particulos$$pdriver 000162226 951__ $$a2025-10-17-14:25:02 000162226 980__ $$aARTICLE