Publications (papers in Scientific Journals and chapters in books)

  1. M. Antoñana, E. Alberdi, J. Makazaga, A. Murua, An implicit symplectic solver for high-precision long term integrations of the Solar System, arXiv:2204.01539, Accepted for publication in Cel. Mech. & Dyn. Astron.
  2. M. Antoñana, P. Chartier, A. Murua, Majorant series for the N-body problem, arXiv:2103.12839, International Journal of Computer Mathematics, 99(1) (2022), 158-183; https://doi.org/10.1080/00207160.2021.1962848
  3. A. Murua, From Runge-Kutta Methods to Hopf Algebras of Rooted Trees, in the series Algebra and Applications 2: Combinatorial Algebra and Hopf Algebras , ISTE Ltd-Wiley 2021;
  4. M. Antoñana, P. Chartier, J. Makazaga, A. Murua, Global time-renormalization of the gravitational N-body problem, arXiv:2001.01221, SIAM J. Appl. Dyn. Syst., 19(4) (2020), 2658-2681; https://doi.org/10.1137/20M1314719
  5. X. Tu, A. Murua, Y. Tang, New high order symplectic integrators via generating functions with its application in many-body problems, Bit Numer Math 60 (2020), 509-534; https://doi.org/10.1007/s10543-019-00785-0
  6. F. Casas, P. Chartier, A. Murua, Continuous changes of variables and the Magnus expansion, Journal of Physics Communications 3 (2019), 095014
  7. R. I. McLachlan and A. Murua, The Lie algebra of classical mechanics, arXiv:1905.07554, J. Comput. Dyn., 6 (2019), 345-360; http://dx.doi.org/10.3934/jcd.2019017
  8. A. Murua, J.M. Sanz-Serna, Hopf algebra techniques to handle dynamical systems and numerical integrators, arXiv 1702.08354, in Computation and Combinatorics in Dynamics, Stochastics and Control, The Abel Symposium, Rosendal, August 2016, E. Celledoni, G. di Nunno, K. Ebrahimi-Fard and H. Z. Munthe-Kaas, eds., Springer, Berkub, 2018, 629-658.
  9. A. Murua, J.M. Sanz-Serna, Averaging and computing normal forms with word series algorithms, arXiv 1512.03601, in Discrete Mechanics, Geometric Integration and Lie-Butcher Series (DMGILBS, Madrid, May 2015), K. Ebrahimi Fard and M. Barbero Liñán eds., Springer, Berlin 2018, 115-137. DOI 978-3-030-01397-4_4.
  10. M. Antoñana, J. Makazaga, A. Murua, New Integration Methods for Perturbed ODEs Based on Symplectic Implicit Runge-Kutta Schemes with Application to Solar System Simulations, arXiv:1711.06050, Journal of Scientific Computing, ISSN 0885-7474, 2018, 76, 1 (2018), pp 630-650, DOI 10.1007/s10915-017-0634-1
  11. M. Antoñana, J. Makazaga, A. Murua, Efficient implementation of symplectic implicit Runge-Kutta schemes with simplified Newton iterations, arXiv 1703.07697, Numerical Algorithms, 78, 1 (2018), pp. 63--86, DOI 10.1007/s11075-017-0367-0
  12. M. Antoñana, J. Makazaga, A. Murua, Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes, Numerical Algorithms 76, 4 (2017), pp. 861--880, doi:10.1007/s11075-017-0287-z
  13. S. Blanes, F. Casas, A. Murua, Symplectic time-average propagators for the Schödinger equation with a time-dependent Hamiltonian, The Journal of Chemical Physics 146, 114109 (2017); doi: 10.1063/1.4978410
  14. A. Murua, J.M. Sanz-Serna, Computing normal forms and formal invariants of dynamical systems by means of word series, Nonlinear Analysis, Theory, Methods and Applications 138 (2016), pp. 326-345.
  15. A. Murua, J.M. Sanz-Serna, Vibrational resonance: a study with high-order word-series averaging, Applied Mathematics and Nonlinear Sciences 1 (2016), pp. 239-146.
  16. A. Murua, J.M. Sanz-Serna, Word series for dynamical systems and their numerical integrators, Foundations of Computational Mathematics (2015), DOI 10.1007/s10208-015-9295-3
  17. S. Blanes, F. Casas, and A. Murua, An efficient algorithm based on splitting for the time integration of the Schrödinger equation, J. Comput. Phys., 303 (2015), pp. 396-412. (Fortran programs)
  18. J.M. Sanz-Serna and A. Murua, Formal series and numerical integrators: some history and some new techniques, in Proceedings of the 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015), Lei Guo and Zhi-Ming eds., Higher Edication, Press, Beijing (2015), pp. 311-331.
  19. A. Murua, (2015) B-Series . In: Engquist B. (eds) Encyclopedia of Applied and Computational Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70529-1_98
  20. S. Blanes, F. Casas, A. Murua (2015) Splitting Methods . In: Engquist B. (eds) Encyclopedia of Applied and Computational Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70529-1_146
  21. F. Castella, P. Chartier, F. Méhats and A. Murua, Stroboscopic averaging for the nonlinear Schrödinger equation , Foundations of Computational Mathematics, Vol. 15, Issue 2 (2015), pp. 519-559.
  22. P. Chartier, A. Murua and J.M. Sanz-Serna, Higher-order averaging, formal series and numerical integration III: error bounds , Foundations of Computational Mathematics, Vol. 15, Issue 2 (2015), pp. 591-612.
  23. P. Chartier, J. Makazaga, A. Murua, and G. Vilmart, Multi-revolution composition methods for highly oscillatory differential equations, Numerische Mathematik 128, 1 (2014), pp. 167-192.
  24. A. Farrés, J. Laskar, S. Blanes, F. Casas, J. Makazaga, and A. Murua, High precision Symplectic Integrators for the Solar System. Cel. Mech. & Dyn. Astron., 116 (2013), pp. 141-174.
  25. S. Blanes, F. Casas, A. Farrés, J. Laskar, J. Makazaga, and A. Murua, New families of symplectic splitting methods for numerical integration in dynamical astronomy, Appl. Numer. Math. 68 (2013), pp. 58-72. arXiv:1208.0689v1
  26. S. Blanes, F. Casas, P. Chartier, and A. Murua, Optimized high-order splitting methods for some classes of parabolic equations, Math. Comput. 82 (2013), pp. 1559-1576.
  27. F. Casas, A. Murua, and M. Nadinic, Efficient computation of the Zassenhaus formula, Computer Physics Communications 183, 11, (2012), 2386-2391.
  28. Ph. Chartier, A. Murua and J. M. Sanz-Serna, Higher-order averaging, formal series and numerical integration II: the quasi-periodic case , Foundations of Computational Mathematics, 12 (2012), 471-508.
  29. Ph. Chartier, A. Murua and J. M. Sanz-Serna, A formal series approach to averaging: exponentially small error estimates , Discrete and Continuous Dynamical Systems 32 (2012), 3009-3027.
  30. S. Blanes, F. Casas, and A. Murua, Splitting methods in the numerical integration of non-autonomous dynamical systems, RACSAM. 106 (2012), 49-66.
  31. S. Blanes, F. Casas, and A. Murua, Error analysis of splitting methods for the time dependent Schrödinger equation , SIAM J. Sci. Comput. 33 (2011), 1525-1548.
  32. M. P. Calvo, Ph. Chartier, A. Murua and J. M. Sanz-Serna, Numerical stroboscopic averaging for ODEs and DAEs , Appl. Numer. Math. 61 (2011), 1077-1095.
  33. M. P. Calvo, Ph. Chartier, A. Murua, and J.M. Sanz-Serna, A stroboscopic method for highly oscillatory problems, in Numerical Analysis and Multiscale Computations, B. Engquist, O. Runborg and R. Tsai, editors, Lect. Notes Comput. Sci. Eng., Vol. 82, Springer 2011, 73-87.
  34. Ph. Chartier, A. Murua and J. M. Sanz-Serna, Higher-order averaging, formal series and numerical integration I: B-series , Found. Comput. Math. 10 (2010), 695-727.
  35. S. Blanes, F. Casas, and A. Murua, Splitting methods with complex coefficients, Bol. Soc. Esp. Mat. Apl. 50 (2010), 47-61.
  36. P. Chartier and A. Murua, An algebraic theory of order , M2AN 43 (2009) 607-630
  37. J. Makazaga, A. Murua, A new class of symplectic integration schemes based on generating functions , Numerische Mathematik, Vol. 113, Issue 4 (2009), 631--642
  38. F. Casas, A. Murua, An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications , Journal of Mathematical Physics 50, 033513 (2009)
  39. S. Blanes, F. Casas, A. Murua, Splitting and Composition Methods in the Numerical Integration of Differential Equations , Bol. Soc. Esp. Mat. Apl. No.45 (2008), 89--145
  40. S. Blanes, F. Casas, A. Murua, On the linear stability of splitting methods , Found Comput Math 8 (2008), 357--393
  41. S. Blanes, F. Casas, A. Murua, Splitting methods for non-autonomous linear systems , Int. J. Comput. Math. 84(6) (2007), 713--727
  42. P. Chartier, A. Murua, Preserving first integrals and volume forms of additively split systems , IMA Journal of Numerical Analysis, vol. 27, 3 (2007), 381--405
  43. S. Blanes, F. Casas, A. Murua, Symplectic operator splitting methods for the time-dependent Schrödinger equation, Journal of Chemical Physics, vol. 124 (2006)
  44. P. Chartier, E. Faou, A. Murua, An algebraic approach to invariant preserving integrators: The case of quadratic and Hamiltonian invariants , Numerische Mathematik, vol. 103 (2006), 575--590
  45. A. Murua, The Hopf algebra of rooted trees, free Lie algebras, and Lie series, Foundations of Computational Mathematics, vol. 6 (2006), 387--426
  46. S. Blanes, F. Casas, A. Murua, Composition methods for differential equations with processing , SIAM Journal of Scientific Computing, vol. 27, No.6 (2006), 1817--1843
  47. S. Blanes, F. Casas, A. Murua, On the numerical integration of ODEs by processed methods, SIAM Journal of Numerical Analysis, vol. 42, No. 2 (2004), 531--552
  48. R.P.K. Chan , P. Chartier and A. Murua, Reversible methods of Runge-Kutta type for Index-2 Differential-Algebraic Equations, Numerische Mathematik, vol. 97, No. 3 (2004), 427--440
  49. J. Makazaga, A. Murua, New Runge-Kutta based schemes for ODEs with cheap global error estimation, Bit Numerical Mathematics, vol 43 (2003), 595-610
  50. R.P.K. Chan , P. Chartier and A. Murua, Post-projected Runge-Kutta methods for index-2 differential-algebraic equations, Applied Numerical Mathematics, 42 (2002) 77-94
  51. R. Chan, A. Murua, Extrapolation of Symplectic methods for Hamiltonian problems, Applied Numerical Mathematics 34 (2000) 189-205
  52. J. Makazaga, A. Murua, Cheap one-step global error estimation for ODEs, New Zeland Journal of Mathematics 29 (2000), 211-221
  53. A. Murua, Formal Series and Numerical integrators. Part I: Systems of ODEs and symplectic Integrators, Applied Numerical Mathematics 29 (1999), 221-251
  54. A. Murua, Formal Series and Numerical integrators. Part II: Application to index 2 differential-algebraic systems, Applied Numerical Mathematics 29 (1999), 99-113
  55. J. M. Sanz-Serna, A. Murua, Order conditions for numerical integrators obtained by composing simpler integrators, Philosophical Transactions of the Royal Society A 357 (1999), 1079-1100
  56. M. Arnold, A. Murua, Non-stiff integrators for differential-algebraic systems of index 2, Numerical Algorithms 19 (1998), 25-41
  57. A. Murua, Runge-Kutta-Nystrom methods for general second order ODEs with application to multi-body systems, Applied Numerical Mathematics (28) 2-4 (1998) 371-386
  58. A. Murua, Order conditions for partitioned symplectic methods, SIAM Journal of Numerical Analysis, Vol 34, No. 6 (1997), 2204-2211
  59. A. Murua, Partitioned half-explicit Runge-Kutta methods for differential-algebraic systems of index 2, Computing, Vol 59, No 1 (1997), 43-61
  60. A. L. Araujo, A. Murua, and J. M. Sanz-Serna, Symplectic methods based on decompositions, SIAM Journal of Numerical Analysis, Vol 34, No. 5 (1997), 1926-1947
  61. E. Hairer, A. Murua, and J. M. Sanz-Serna, The non-existence of symplectic multi-derivative Runge-Kutta methods, BIT 34 (1994), 80-87
  62. M. P. Calvo, A. Murua, and J. M. Sanz-Serna, Modified equations for ODEs, Contentemporary Mathematics, Vol 172, American Mathematical Society (1994), 63-74
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