New families of symplectic splitting methods for numerical integration in dynamical astronomy S Blanes, F Casas, A Farres, J Laskar, J Makazaga, A Murua
Applied Numerical Mathematics 68, 58-72, 2013
114 2013 High precision symplectic integrators for the Solar System A Farrés, J Laskar, S Blanes, F Casas, J Makazaga, A Murua
Celestial Mechanics and Dynamical Astronomy 116 (2), 141-174, 2013
73 2013 Multi-revolution composition methods for highly oscillatory differential equations P Chartier, J Makazaga, A Murua, G Vilmart
Numerische Mathematik 128, 167-192, 2014
30 2014 Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes M Antoñana, J Makazaga, A Murua
Numerical Algorithms 76 (4), 861-880, 2017
15 2017 New Runge–Kutta based schemes for ODEs with cheap global error estimation J Makazaga, A Murua
BIT Numerical Mathematics 43, 595-610, 2003
15 2003 A new class of symplectic integration schemes based on generating functions J Makazaga, A Murua
Numerische Mathematik 113 (4), 631-642, 2009
7 2009 Efficient implementation of symplectic implicit Runge-Kutta schemes with simplified Newton iterations M Antoñana, J Makazaga, A Murua
Numerical Algorithms 78 (1), 63-86, 2018
6 2018 Cheap one-step global error estimation for odes A Murua, J Makazaga
New Zealand journal of mathematics 29, 211-221, 2000
5 2000 New Integration Methods for Perturbed ODEs Based on Symplectic Implicit Runge–Kutta Schemes with Application to Solar System Simulations M Antoñana, J Makazaga, A Murua
Journal of Scientific Computing 76 (1), 630-650, 2018
4 2018 Global Time-Renormalization of the Gravitational M Antoñana, P Chartier, J Makazaga, A Murua
SIAM Journal on Applied Dynamical Systems 19 (4), 2658–2681, 2020
3 2020 Global Time-Renormalization of the Gravitational M Anton͂ana, P Chartier, J Makazaga, A Murua
SIAM Journal on Applied Dynamical Systems 19 (4), 2658-2681, 2020
3 2020 An implicit symplectic solver for high-precision long-term integrations of the Solar System M Antoñana, E Alberdi, J Makazaga, A Murua
Celestial Mechanics and Dynamical Astronomy 134 (3), 31, 2022
2 2022 An algorithm based on continuation techniques for minimization problems with highly non-linear equality constraints E Alberdi, M Antoñana, J Makazaga, A Murua
arXiv preprint arXiv:1909.07263, 2019
2 2019 Sobre los errores locales y globales de la integración de Ecuaciones Diferenciales Ordinarias mediante métodos de Runge-Kutta Explícitos J Makazaga Odria
UPV/EHU (University of the Basque Country) Departmnet KZAA/CCIA (Computer …, 2007
1 2007 Taylor-Fourier integration MP Calvo, J Makazaga, A Murua
arXiv preprint arXiv:2406.03124, 2024
2024 Implicit symplectic methods for high precision numerical integration of the Solar System E Alberdi, M Antonana, J Makazaga, A Murua
Conference on Applied and Industrial Mathematics, 44-45, 2022
2022 An algorithm based on continuation techniques for minimization problems with non-linear equality constraints E Alberdi, J Makazaga, A Murua, M Antonana
Proceedings IMCS-55, 176-178, 2019
2019 Integratzaile simetrikodun 10 ordenako konposizio metodo simetrikoen bilaketa (Search of 10-order symmetric composition methods of symmetric integrators) E Alberdi Celaya, J Makazaga Odria, A Murua Uria
Ekaia. EHUko Zientzia eta Teknologia aldizkaria- ISSN: 0214-9001 34, 99-121, 2018
2018 Technique to find 10-order Symmetric Composition Methods of Symmetric Integrators EA Celaya, J Makazaga, A Murua
Congress on Numerical Methods in Engineering CMN2017 3, 5, 2017
2017 Search of symmetric composition methods of symmetric integrators E Alberdi Celaya
2016 
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