Back to Main Page	Joseba Makazaga Member of Mathematical Modeling, Statistics and Optimization (MATHMODE) research group OrcID, ResearchGate
Research

Publications Calvo, M. P.; Makazaga, J.; Murua, A. Taylor-Fourier Approximation, J Sci Comput (Journal of Scientific Computing) 103, 69 (2025). DOI 10.1007/s10915-025-02880-7 (preprint ArXiv) Antoñana, M.;Alberdi, E.; Makazaga, J. & Murua, A. An implicit symplectic solver for high-precision long-term integrations of the Solar System, Celest Mech Dyn Astron (Celestial Mechanics and Dynamical Astronomy), ISSN 0923-2958, Volume 134,issue 3, 2022. DOI https://doi.org/10.1007/s10569-022-10081-9 Alberdi, E.; Antoñana, M.; Makazaga, J. & Murua, A. An algorithm based on continuation techniques for minimization problems with highly non-linear equality constraints, Preprint Arxiv, 2019. DOI 10.48550/arxiv.1909.07263 Antoñana, Mikel; Chartier, Philippe; Makazaga, Joseba & Murua, Ander. Global Time-Renormalization of the Gravitational N-body Problem, SIAM Journal on Applied Dynamical Systems, ISSN 1536-0040, Vol. 19, No. 4, pp. 2658--2681, 2020. DOI https://doi.org/10.1137/20M1314719 Alberdi E., Makazaga, J. & Murua, A. Integratzaile simetrikodun 10 ordenako konposizio metodo simetrikoen bilaketa, Ekaia. Euskal Herriko Unibertsitateko zientzi eta teknologi aldizkaria, ISSN: 0214-9001, vol. 34, pages 99-121, 2018. DOI 10.1387/ekaia.19341 Antoñana, M., Makazaga, J. & Murua, A. New Integration Methods for Perturbed ODEs Based on Symplectic Implicit Runge-Kutta Schemes with Application to Solar System Simulations, Journal of Scientific Computing, ISSN 0885-7474, 2018, vol 76, number 1, pages 630-650, July 2018, DOI 10.1007/s10915-017-0634-1 Antoñana, M., Makazaga, J. & Murua, A. Efficient implementation of symplectic implicit Runge-Kutta schemes with simplified Newton iterations , Numerical Algorithms, 2018, vol 78, issue 1, pages 63--86, Received: 22 March 2017 / Accepted: 19 June 2017/ Published online: 28 June 2017, DOI 10.1007/s11075-017-0367-0 Antoñana, M., Makazaga, J. & Murua, A. Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes , Numerical Algorithms, 2017, vol. 76, issue 4, pages 861--880, December 2017, DOI:10.1007/s11075-017-0287-z Philippe Chartier, Joseba Makazaga, Ander Murua, Gilles Vilmart. Multi-revolution composition methods for highly oscillatory differential equations, Numerische Mathematik, September 2014, Volume 128, issue 1, pages 167--192, Received: 4 March 2013 / Revised: 20 September 2013/ Published online: 17 January 2014, DOI 10.1007/s00211-013-0602-0 Ariadna Farrés, Jacques Laskar, Sergio Blanes, Fernando Casas, Joseba Makazaga, Ander Murua. High precision symplectic integrators for the Solar System, Celestial Mechanics and Dynamical Astronomy, Received: 6 August 2012 / Revised: / Accepted: 27 February 2013, DOI 10.1007/s10569-013-9479-6 S. Blanes, F. Casas, A. Farrés, J. Laskar, J. Makazaga, A. Murua. New families of symplectic splitting methods for numerical integration in dynamical astronomy, Applied Numerical Mathematics, Volume 68, June 2013, Pages 58-72, ISSN 0168-9274, 10.1016/j.apnum.2013.01.003. J. Makazaga, A. Murua, A new class of symplectic integration schemes based on generating functions , Numerische Mathematik, Vol. 113, Issue 4 (2009), Page 631--642 doi: 10.1007/s00211-009-0243-5 J. Makazaga, A. Murua. New Runge-Kutta based schemes for ODEs with cheap global error estimation. BIT Nummerical Mathematics Vol. 43 #3 (Sept 2003), 595-610 doi: 10.1023/B:BITN.0000007056.32638.fb A. Murua, J. Makazaga. Cheap one-step global error estimation for ODEs. New Zealand Journal of Mathematics, Vol 29, Issue 2, (october 2000), pages 211-221. ISSN 1179-4984 Preprint version PhD Sobre los errores locales y globales de la integración de Ecuaciones Diferenciales Ordinarias mediante métodos de Runge-Kutta Explícitos. Julio 2007. publicación: Resolución de Ecuaciones Diferenciales mediante métodos de Runge-Kutta: Estudio de los errores locales y globales en la integración de EDOs mediante métodos de Runge-Kutta Explícitos. EAE (Editorial Académica Española), ISBN 978-3-8454-9462-3, (2011) 148 páginas Other publications J. Makazaga, A. Lasa. Ordenadore Bidezko Irudigintza Udako Euskal Unibertsitatea, ISBN 84-86967-90-2, Bilbo 1998. Interests Global Error Estimation for ODE solver Numerical Integration of Hamiltonian systems Step-size selection Parallel computing Computer Graphics