132869 20260217205511.0 doi 10.1016/j.cam.2023.115533 sideral 137681 ART-2024-137681 eng Montijano, J. I. Universidad de Zaragoza (orcid)0000-0001-6120-4427 Explicit Runge–Kutta–Nyström methods for the numerical solution of second order linear inhomogeneous IVPs 2024 Access copy available to the general public Unrestricted Runge–Kutta–Nyström (RKN) methods for the numerical solution of inhomogeneous linear initial value problems with constant coefficients are considered. A general procedure to construct explicit-stage RKN methods with maximal order [fórmula], similar to the developed by the authors (Montijano et al., 2023) for the class of second order IVP under consideration, depending on the nodes [fórmula] is presented. This procedure requires only the solution of successive linear equations in the element<sub>ij, [fórmula], of the matrix of coefficients A of the RKN method and avoids the solution of non linear equations. The remarkable fact is that using as free parameters the nodes [fórmula] with a quadrature relation, the [fórmula] elements of matrix can be computed by solving successively linear systems with coefficients depending on the nodes, so that if they are non-singular we get a unique 8-stage method with maximal order [fórmula]. We obtain an optimized six-stage seventh-order RKN method in the sense that the nodes are chosen so that minimize the leading term of the local error. Finally, some numerical experiments are presented to test the behaviour of the optimized RKN method with others with Radau and Lobatto nodes. info:eu-repo/grantAgreement/ES/MICINN/PID2019-109045GB-C31 info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es 2.6 2024 MATHEMATICS, APPLIED 35 / 344 = 0.102 2024 Q1 T1 0.688 2024 Computational Mathematics 2024 Q2 Applied Mathematics 2024 Q2 4.8 2024 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Rández, L. Universidad de Zaragoza (orcid)0000-0002-4238-3228 Calvo, M. (orcid)0000-0002-3312-5710 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 438 (2024), 115533 [19 pp.] J. comput. appl. math. Journal of Computational and Applied Mathematics 0377-0427 491231 http://zaguan.unizar.es/record/132869/files/texto_completo.pdf Versión publicada 1723618 http://zaguan.unizar.es/record/132869/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:132869 articulos driver 2026-02-17-20:25:03 ARTICLE