Yang, Hongli; Zeng, Xianyang The tri-coloured free-tree theory for symplectic multi-frequency ERKN methods. (English) Zbl 1502.65043 J. Comput. Appl. Math. 423, Article ID 114964, 20 p. (2023). MSC: 65L06 65L05 65P10 PDFBibTeX XMLCite \textit{H. Yang} and \textit{X. Zeng}, J. Comput. Appl. Math. 423, Article ID 114964, 20 p. (2023; Zbl 1502.65043) Full Text: DOI
Famelis, Ioannis Th.; Tsitouras, Ch. Symbolic derivation of Runge-Kutta-Nyström type order conditions and methods for solving \(y''' = f(x, y)\). (English) Zbl 1411.65094 Appl. Math. Comput. 297, 50-60 (2017). MSC: 65L06 65L05 68W30 34A34 PDFBibTeX XMLCite \textit{I. Th. Famelis} and \textit{Ch. Tsitouras}, Appl. Math. Comput. 297, 50--60 (2017; Zbl 1411.65094) Full Text: DOI
Benner, Peter; Hess, Martin Reduced basis approximations for Maxwell’s equations in dispersive media. (English) Zbl 1388.78018 Benner, Peter (ed.) et al., Model reduction of parametrized systems. Selected contributions based on the presentations at the MoRePaS conference, SISSA, Trieste, Italy, October 13–16, 2015. Cham: Springer (ISBN 978-3-319-58785-1/hbk; 978-3-319-58786-8/ebook). MS&A. Modeling, Simulation and Applications 17, 107-119 (2017). MSC: 78M34 78A40 78A50 35Q60 35L10 68T20 PDFBibTeX XMLCite \textit{P. Benner} and \textit{M. Hess}, MS\&A, Model. Simul. Appl. 17, 107--119 (2017; Zbl 1388.78018) Full Text: DOI
Yang, Hongli; Zeng, Xianyang A feasible and effective technique in constructing ERKN methods for multi-frequency multidimensional oscillators in scientific computation. (English) Zbl 1421.65018 Numer. Algorithms 76, No. 3, 761-782 (2017). Reviewer: Raffaella Pavani (Milano) MSC: 65L06 65L05 PDFBibTeX XMLCite \textit{H. Yang} and \textit{X. Zeng}, Numer. Algorithms 76, No. 3, 761--782 (2017; Zbl 1421.65018) Full Text: DOI
Famelis, I. Th.; Tsitouras, Ch. On modifications of Runge-Kutta-Nyström methods for solving \(y^{(4)} = f(x, y)\). (English) Zbl 1410.65248 Appl. Math. Comput. 273, 726-734 (2016). MSC: 65L05 65L06 68W30 PDFBibTeX XMLCite \textit{I. Th. Famelis} and \textit{Ch. Tsitouras}, Appl. Math. Comput. 273, 726--734 (2016; Zbl 1410.65248) Full Text: DOI
Kalogiratou, Z.; Monovasilis, Th.; Psihoyios, G.; Simos, T. E. Runge-Kutta type methods with special properties for the numerical integration of ordinary differential equations. (English) Zbl 1360.65194 Phys. Rep. 536, No. 3, 75-146 (2014). MSC: 65L06 65P10 37M15 65L05 65L15 PDFBibTeX XMLCite \textit{Z. Kalogiratou} et al., Phys. Rep. 536, No. 3, 75--146 (2014; Zbl 1360.65194) Full Text: DOI
Wang, Bin; Wu, Xinyuan A highly accurate explicit symplectic ERKN method for multi-frequency and multidimensional oscillatory Hamiltonian systems. (English) Zbl 1291.65362 Numer. Algorithms 65, No. 3, 705-721 (2014). MSC: 65P10 37M15 65L06 PDFBibTeX XMLCite \textit{B. Wang} and \textit{X. Wu}, Numer. Algorithms 65, No. 3, 705--721 (2014; Zbl 1291.65362) Full Text: DOI
Tsitouras, Ch.; Famelis, I. Th. Symbolic derivation of Runge-Kutta-Nyström order conditions. (English) Zbl 1185.65127 J. Math. Chem. 46, No. 3, 896-912 (2009). MSC: 65L06 65L05 34A34 34-04 PDFBibTeX XMLCite \textit{Ch. Tsitouras} and \textit{I. Th. Famelis}, J. Math. Chem. 46, No. 3, 896--912 (2009; Zbl 1185.65127) Full Text: DOI
Xiao, Aiguo; Tang, Yifa Order properties of symplectic Runge-Kutta-Nyström methods. (English) Zbl 1155.65396 Comput. Math. Appl. 47, No. 4-5, 569-582 (2004). MSC: 65P10 37M15 65L06 PDFBibTeX XMLCite \textit{A. Xiao} and \textit{Y. Tang}, Comput. Math. Appl. 47, No. 4--5, 569--582 (2004; Zbl 1155.65396) Full Text: DOI
Iserles, Arieh; Ramaswami, Geetha; Sofroniou, Mark Runge-Kutta methods for quadratic ordinary differential equations. (English) Zbl 0908.65063 BIT 38, No. 2, 315-346 (1998). Reviewer: E.Hairer (Genève) MSC: 65L06 65L05 34A34 PDFBibTeX XMLCite \textit{A. Iserles} et al., BIT 38, No. 2, 315--346 (1998; Zbl 0908.65063) Full Text: DOI
Burnton, Christopher; Scherer, Rudolf Gauss-Runge-Kutta-Nyström methods. (English) Zbl 0904.65076 BIT 38, No. 1, 12-21 (1998). Reviewer: A.Marciniak (Poznań) MSC: 65L06 65L05 37J99 65L20 PDFBibTeX XMLCite \textit{C. Burnton} and \textit{R. Scherer}, BIT 38, No. 1, 12--21 (1998; Zbl 0904.65076) Full Text: DOI
Calvo, M. P.; Hairer, E. Further reduction in the number of independent order conditions for symplectic, explicit partitioned Runge-Kutta and Runge-Kutta-Nyström methods. (English) Zbl 0885.65087 Appl. Numer. Math. 18, No. 1-3, 107-114 (1995). Reviewer: J.C.Butcher (Auckland) MSC: 65L06 37-XX 65L05 34A34 PDFBibTeX XMLCite \textit{M. P. Calvo} and \textit{E. Hairer}, Appl. Numer. Math. 18, No. 1--3, 107--114 (1995; Zbl 0885.65087) Full Text: DOI
Franco, J. M. An explicit hybrid method of Numerov type for second-order periodic initial-value problems. (English) Zbl 0844.65061 J. Comput. Appl. Math. 59, No. 1, 79-90 (1995). Reviewer: J.B.Butler jun.(Portland) MSC: 65L06 65L05 34C25 34A34 PDFBibTeX XMLCite \textit{J. M. Franco}, J. Comput. Appl. Math. 59, No. 1, 79--90 (1995; Zbl 0844.65061) Full Text: DOI
Portillo, A.; Sanz-Serna, J. M. Lack of dissipativity is not symplecticness. (English) Zbl 0844.65062 BIT 35, No. 2, 269-276 (1995). Reviewer: J.B.Butler jun.(Portland) MSC: 65L06 65L05 37-XX PDFBibTeX XMLCite \textit{A. Portillo} and \textit{J. M. Sanz-Serna}, BIT 35, No. 2, 269--276 (1995; Zbl 0844.65062) Full Text: DOI
Okunbor, Daniel I.; Skeel, Robert D. Canonical Runge-Kutta-Nyström methods of orders five and six. (English) Zbl 0872.65067 J. Comput. Appl. Math. 51, No. 3, 375-382 (1994). MSC: 65L06 65L05 34A34 37-XX PDFBibTeX XMLCite \textit{D. I. Okunbor} and \textit{R. D. Skeel}, J. Comput. Appl. Math. 51, No. 3, 375--382 (1994; Zbl 0872.65067) Full Text: DOI
Calvo, M. P.; Sanz-Serna, J. M. Order conditions for canonical Runge-Kutta-Nyström methods. (English) Zbl 0802.65089 BIT 32, No. 1, 131-142 (1992). Reviewer: U.Göhner (Leonberg) MSC: 65L06 65L05 37-XX 70H15 PDFBibTeX XMLCite \textit{M. P. Calvo} and \textit{J. M. Sanz-Serna}, BIT 32, No. 1, 131--142 (1992; Zbl 0802.65089) Full Text: DOI
Sanz-Serna, J. M. Symplectic Runge-Kutta and related methods: Recent results. (English) Zbl 0779.58019 Physica D 60, No. 1-4, 293-302 (1992). MSC: 37J99 PDFBibTeX XMLCite \textit{J. M. Sanz-Serna}, Physica D 60, No. 1--4, 293--302 (1992; Zbl 0779.58019) Full Text: DOI