000132869 001__ 132869
000132869 005__ 20240315113108.0
000132869 0247_ $$2doi$$a10.1016/j.cam.2023.115533
000132869 0248_ $$2sideral$$a137681
000132869 037__ $$aART-2024-137681
000132869 041__ $$aeng
000132869 100__ $$0(orcid)0000-0001-6120-4427$$aMontijano, J. I.$$uUniversidad de Zaragoza
000132869 245__ $$aExplicit Runge–Kutta–Nyström methods for the numerical solution of second order linear inhomogeneous IVPs
000132869 260__ $$c2024
000132869 5060_ $$aAccess copy available to the general public$$fUnrestricted
000132869 5203_ $$aRunge–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.
000132869 536__ $$9info:eu-repo/grantAgreement/ES/MICINN/PID2019-109045GB-C31
000132869 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/
000132869 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000132869 700__ $$0(orcid)0000-0002-4238-3228$$aRández, L.$$uUniversidad de Zaragoza
000132869 700__ $$0(orcid)0000-0002-3312-5710$$aCalvo, M.
000132869 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000132869 773__ $$g438 (2024), 115533 [19 pp.]$$pJ. comput. appl. math.$$tJournal of Computational and Applied Mathematics$$x0377-0427
000132869 8564_ $$s491231$$uhttps://zaguan.unizar.es/record/132869/files/texto_completo.pdf$$yVersión publicada
000132869 8564_ $$s1723618$$uhttps://zaguan.unizar.es/record/132869/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000132869 909CO $$ooai:zaguan.unizar.es:132869$$particulos$$pdriver
000132869 951__ $$a2024-03-15-08:51:39
000132869 980__ $$aARTICLE