Papers in Scientific Journals

  1. E. S. Carlin, S. Blanes, and F. Casas. Reformulating polarized radiative transfer for astrophysical applications (I). A formalism allowing non-local Magnus solutions. The Open Journal of Astrophysics 8 (2025) (pdf).
  2. F. Casas, A. Escorihuela-Tomŕs, and P. A. Moreno Casares. Approximating exponentials of commutators by optimized product formulas. Quantum Information Processing 24 (2025),47 (pdf).
  3. S. Blanes, F. Casas, and A. Murua. Splitting methods for differential equations. Acta Numerica 33 (2024),1-161 (pdf).
  4. S. Blanes, F. Casas, and L. Shaw. Generalized extrapolation methods based on compositions of a basic 2nd-order scheme. Applied Mathematics and Computation 473 (2024),128663 (pdf).
  5. S. Blanes, F. Casas, and A. Escorihuela-Tomŕs. Families of efficient low order processed composition methods. Applied Numerical Mathematics 204 (2024),86-100 (pdf).
  6. S. Blanes, F. Casas, C. González, and M. Thalhammer. Symmetric-conjugate splitting methods for evolution equations of parabolic type. Journal of Computational Dynamics 11 (2024),108-134 (pdf).
  7. S. Blanes, F. Casas, C. González, and M. Thalhammer. Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type. Computer Physics Communications 295 (2024),109007 (pdf).
  8. J. Bernier, S. Blanes, F. Casas, and A. Escorihuela-Tomŕs. Symmetric-conjugate splitting methods for linear unitary problems. BIT Numerical Mathematics 63 (2023),58 (pdf).
  9. S. Blanes, F. Casas, C. González, and M. Thalhammer. Efficient splitting methods based on modified potentials: numerical integration of linear parabolic problems and imaginary time propagation of the Schrödinger equation. Communications in Computational Physics 33 (2023),937-961 (pdf).
  10. F. Casas, J.M. Sanz-Serna, and L. Shaw. A new optimality property of Strang's splitting. SIAM Journal on Numerical Analysis 61 (2023),1369-1385 (pdf).
  11. F. Casas, J.M. Sanz-Serna, and L. Shaw. Split Hamiltonian Monte Carlo revisited. Statistics and Computing 32 (2022), 86 (pdf).
  12. S. Blanes, F. Casas, and A. Escorihuela-Tomŕs. Runge-Kutta-Nyström symplectic splitting methods of order 8. Applied Numerical Mathematics 182 (2022), 14-27 (pdf).
  13. S. Blanes, F. Casas, P. Chartier, and A. Escorihuela-Tomŕs. On symmetric-conjugate composition methods in the numerical integration of differential equations. Mathematics of Computation 91 (2022), 1739-1761 (pdf).
  14. S. Blanes, F. Casas, and A. Escorihuela-Tomŕs. Applying splitting methods with complex coefficients to the numerical integration of unitary problems. Journal of Computational Dynamics 9 (2022), 85-101 (pdf).
  15. P. Bader, S. Blanes, F. Casas, and M. Seydaoglu. An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrödinger equation. Mathematics and Computers in Simulation 194 (2022), 383-400 (pdf).
  16. F. Casas, and A. Escorihuela-Tomŕs. High order integrators obtained by linear combinations of symmetric-conjugate compositions. Applied Mathematics and Computation 414 (2022), 126700 (pdf).
  17. S. Blanes, M.P. Calvo, F. Casas, and J.M. Sanz-Serna. Symmetrically processed splitting integrators for enhanced Hamiltonian Monte Carlo sampling. SIAM Journal on Scientific Computing 43 (2021), A3357-A3371 (pdf).
  18. A. Arnal, F. Casas, and C. Chiralt. A note on the Baker-Campbell-Hausdorff series in terms of right-nested commutators. Mediterranean Journal of Mathematics 18 (2021), 53 (pdf).
  19. A. Arnal, F. Casas, C. Chiralt, and J.A. Oteo. A unifying framework for perturbative exponential factorizations. Mathematics 9 (2021), 637 (pdf).
  20. F. Casas, P. Chartier, A. Escorihuela-Tomŕs, and Y. Zhang. Compositions of pseudo-symmetric integrators with complex coefficients for the numerical integration of differential equations. Journal of Computational and Applied Mathematics 381 (2021), 113006 (pdf).
  21. M. Seydaoglu, P. Bader, S. Blanes, and F. Casas. Computing the matrix sine and cosine simultaneously with a reduced number of products. Applied Numerical Mathematics 163  (2021), 96-107 (pdf).
  22. S. Blanes, F. Casas, C. González and M. Thalhammer. Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear Schrödinger equations. IMA Journal of Numerical Analysis 41 (2021), 594-617 (pdf).
  23. A. Arnal, F. Casas and C. Chiralt. Exponential perturbative expansions and coordinate transformations. Mathematical and Computational Applications 25 (2020), 50 (pdf).
  24. J. Bernier, F. Casas and N. Crouseilles. Splitting methods for rotations: application to Vlasov equations. SIAM Journal on Scientific Computing 42 (2020), A666-697 (pdf).
  25. F. Casas, A. Escorihuela-Tomŕs. Composition methods for dynamical systems separable into three parts. Mathematics 8 (2020), 533 (pdf).
  26. M. Hajiketabi, F. Casas. Numerical integrators based on the Magnus expansion for nonlinear dynamical systems. Applied Mathematics and Computation 369 (2020), 124844 (pdf).
  27. P. Bader, S. Blanes, F. Casas. Computing the matrix exponential with an optimized Taylor polynomial approximation. Mathematics 7 (2019), 1174 (pdf).  
  28. P. Bader, S. Blanes, F. Casas, M. Thalhammer. Efficient time integration methods for Gross-Pitaevskii equations with rotation term. Journal of Computational Dynamics 6 (2019), 147-169 (pdf).
  29. F. Casas, P. Chartier, A. Murua. Continuous changes of variables and the Magnus expansion. Journal of Physics Communications 3 (2019), 095014 (pdf).
  30. S. Blanes, F. Casas, M. Thalhammer. Splitting and composition methods with embedded error estimators. Applied Numerical Mathematics 146 (2019), 400-415 (pdf).
  31. P. Bader, S. Blanes, F. Casas, N. Kopylov. Symplectic propagators for the Kepler problem with time-dependent mass. Celestial Mechanics and Dynamical Astronomy 131 (2019), 25 (pdf).
  32. P. Bader, S. Blanes, F. Casas, N. Kopylov. Novel symplectic integrators for the Klein-Gordon equation with space- and time-dependent mass. Journal of Computational and Applied Mathematics 350 (2019), 130-138. (pdf)
  33. A. Arnal, F. Casas and C. Chiralt. A general formula for the Magnus expansion in terms of iterated integrals of right-nested commutators. Journal of Physics Communications 2 (2018), 035024. (pdf)
  34. P. Bader, S. Blanes, F. Casas, N. Kopylov and E. Ponsoda. Symplectic integrators for second-order linear non-autonomous equations. Journal of Computational and Applied Mathematics 330 (2018), 909-919. (pdf)
  35. M. Hajiketabi, S. Abbasbandy and F. Casas. The Lie-group method based on radial basis functions for solving nonlinear high dimensional generalized Benjamin-Bona-Mahony-Burgers equation in arbitrary domains. Applied Mathematics and Computation 321 (2018), 223-243. (pdf)
  36. S. Blanes, F. Casas and M. Thalhammer. Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear evolution equations of parabolic type. IMA Journal of Numerical Analysis 38 (2018), 743-778. (pdf)
  37. A. Arnal, F. Casas and C. Chiralt. A note on trigonometric identities involving non-commuting matrices. SEMA Journal 75 (2018), 35-44. (pdf)
  38. S. Blanes, F. Casas and M. Thalhammer. High-order commutator-free quasi-Magnus exponential integrators for non-autonomous linear evolution equations.
    Computer Physics Communications 220 (2017), 243-262. (pdf)
  39. A. Arnal, F. Casas and C. Chiralt. On the structure and convergence of the symmetric Zassenhaus formula. Computer Physics Communications 217 (2017), 58-65. (pdf)
  40. S. Blanes, F. Casas and A. Murua. Symplectic time-average propagators for the Schrödinger equation with a time-dependent Hamiltonian. The Journal of Chemical Physics 146 (2017), 114109. (pdf)
  41. F. Casas, N. Crouseilles, E. Faou and M. Mehrenberger. High-order Hamiltonian splitting for the Vlasov-Poisson equations. Numerische Mathematik 135 (2017), 769-801. (pdf)
  42. F. Casas, J.C. D'Olivo and J.A. Oteo. Efficient numerical integration of neutrino oscillations in matter. Physical Review D 94 (2016), 113008. (pdf)
  43. P. Bader, S. Blanes, F. Casas and E. Ponsoda. Efficient numerical integration of Nth-order non-autonomous linear differential equations. Journal of Computational and Applied Mathematics 291 (2016), 380-390. (pdf)
  44. A. Arnal, F. Casas and C. Chiralt. A perturbative algorithm for quasi-periodic linear systems close to constant coefficients. Applied Mathematics and Computation 273 (2016), 398-409. (pdf)
  45. S. Blanes, F. Casas, and A. Murua. An efficient algorithm based on splitting for the time integration of the Schrödinger equation. Journal of Computational Physics 303 (2015), 396-412. (pdf)
  46. F. Casas. On time-dependent perturbation theory in matrix mechanics and time averaging. European Journal of Physics 36 (2015), 055049. (pdf)
  47. B. Afeyan, F. Casas, N. Crouseilles, A. Dodhy, E. Faou, M. Mehrenberger, and E. Sonnendrücker. Simulations of Kinetic Electrostatic Electron Nonlinear (KEEN) waves with variable velocity resolution grids and high-order time-splitting. European Physical Journal D 68 (2014), 295. (pdf)
  48. S. Blanes, F. Casas and J.M. Sanz-Serna. Numerical integrators for the Hybrid Monte Carlo method. SIAM Journal on Scientific Computing 36 (2014), A1556-A1580.  (pdf)
  49. A. Arnal and F. Casas. Exponential polar factorization of the fundamental matrix of linear differential equations. Journal of Computational and Applied Mathematics 268 (2014), 168-178. (pdf)
  50. F. Casas and C. Chiralt. A Lie-Deprit perturbation algorithm for linear differential equations with periodic coefficients. Discrete and Continuous Dynamical Systems 34 (2014), 959-975. (pdf)  
  51. P. Bader, S. Blanes and F. Casas. Solving the Schrödinger eigenvalue problem by the imaginary time propagation technique using splitting methods with complex coefficients. The Journal of Chemical Physics 139 (2013), 124117 (pdf). 
  52. S. Blanes, F. Casas, P. Chartier and A. Murua. Optimized high-order splitting methods for some classes of parabolic equations. Mathematics of Computation 82 (2013), 1559-1576 (pdf).
  53. 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. Applied Numerical Mathematics 68 (2013), 58-72 (pdf).
  54. A. Farrés, J. Laskar, S. Blanes, F. Casas, J. Makazaga and A. Murua. High precision Symplectic Integrators for the Solar System. Celestial Mechanics and Dynamical Astronomy 116 (2013), 141-174 (pdf).
  55. F. Casas, A. Murua and M. Nadinic. Efficient computation of the Zassenhaus formula. Computer Physics Communications 183 (2012), 2386-2391. (pdf)
  56. S. Blanes, F. Casas and A. Murua. Splitting methods in the numerical integration of non-autonomous dynamical systems. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas (RACSAM) 106 (2012), 49-66. (pdf)
  57. F. Casas, J.A. Oteo and J. Ros. Unitary transformations depending on a small parameter. Proceedings of the Royal Society A. Mathematical, Physical & Engineering Sciences 468 (num. 2139) (2012), 685-700. (pdf)
  58. S. Sánchez, F. Casas and A. Fernández. New analytic approximations based on the Magnus expansion. Journal of Mathematical Chemistry 49 (2011), 1741-1758. (pdf)
  59. S. Blanes, F. Casas and A. Murua. Error analysis of splitting methods for the time dependent Schrödinger equation. SIAM Journal on Scientific Computing 33 (2011), 1525-1548. (pdf)
  60. F. Casas. On processed splitting methods and high-order actions in path-integral Monte Carlo simulations. The Journal of Chemical Physics 133 (2010), 154114 (10 pages). (pdf)
  61. S. Blanes, F. Casas, J.A. Oteo and J. Ros. A pedagogical approach to the Magnus expansion. European Journal of Physics 31 (2010), 907-918. (pdf)
  62. F. Casas and A. Murua. An efficient algorithm for computing the Baker-Campbell-Hausdorff series and some of its applications. Journal of Mathematical Physics 50 (2009), 033513. (pdf)
  63. S. Blanes, F. Casas, J.A. Oteo and J. Ros. The Magnus expansion and some of its applications. Physics Reports 470 (2009), 151-238. (pdf)
  64. S. Blanes, F. Casas and A. Murua. Splitting and composition methods in the numerical integration of differential equations. Boletín de la Sociedad Espańola de Matemática Aplicada 45 (2008), 89-145. (pdf)
  65. S. Blanes, F. Casas and A. Murua. On the linear stability of splitting methods. Foundations of Computational Mathematics 8 (2008), 357-393. (pdf)
  66. F. Casas. Sufficient conditions for the convergence of the Magnus expansion. Journal of Physics A: Mathematical and Theoretical 40 (2007), 15001-15017. (pdf)
  67. S. Blanes, F. Casas and A. Murua. Splitting methods for non-autonomous linear systems. International Journal of Computer Mathematics 84 (2007), 713-727. (pdf)
  68. F. Casas. New numerical integrators based on solvability and splitting. Journal of Computational and Applied Mathematics 205 (2007), 802-813. (pdf)
  69. S. Blanes, F. Casas and A. Murua. Symplectic splitting operator methods for the time-dependent Schrödinger equation. The Journal of Chemical Physics 124 (2006), 234105. (pdf)
  70. F. Casas and A. Iserles. Explicit Magnus expansions for nonlinear equations. Journal of Physics A: Mathematical and General 39 (2006), 5445-5461. (pdf)
  71. S. Blanes and F. Casas. Splitting methods for non-autonomous separable dynamical systems. Journal of Physics A: Mathematical and General 39 (2006), 5405-5423. (pdf)
  72. S. Blanes, F. Casas and A. Murua. Composition methods for differential equations with processing. SIAM Journal on Scientific Computing 27 (2006), 1817-1843. (pdf)
  73. S. Blanes and F. Casas. On the necessity of negative coefficients for operator splitting schemes of order higher than two. Applied Numerical Mathematics 54 (2005), 23-37. (pdf)
  74. S. Blanes and F. Casas. Raising the order of geometric numerical integrators by composition and extrapolation. Numerical Algorithms 38 (2005), 305-326. (pdf)
  75. S. Blanes and F. Casas. On the convergence and optimization of the Baker-Campbell-Hausdorff formula. Linear Algebra and its Applications 376 (2004), 135-158. (pdf)
  76. F. Casas. Numerical integration methods for the double-bracket flow. Journal of Computational and Applied Mathematics 166 (2004), 477-495. (pdf)
  77. S. Blanes, F. Casas and A. Murua. On the numerical integration of ordinary differential equations by processed methods. SIAM Journal on Numerical Analysis 42 (2004), 531-552. (pdf)
  78. F. Casas and B. Owren. Cost efficient Lie group integrators in the RKMK class. BIT. Numerical Mathematics 43 (2003), 723-742. (pdf)
  79. S. Blanes and F. Casas. Optimization of Lie group methods for differential equations. Future Generation Computer Systems 19 (2003), 331-339. (pdf)
  80. J. Wensch and F. Casas. Extrapolation in Lie groups with approximated BCH-formula. Applied Numerical Mathematics 42 (2002), 465-472. (pdf)
  81. S. Blanes, F. Casas and J. Ros. Optimized geometric integrators of higher order for linear differential equations. BIT 42 (2002), 262-284. (pdf)
  82. S. Blanes, F. Casas and J. Ros. High order Runge-Kutta-Nyström geometric methods with processing. Applied Numerical Mathematics 39 (2001), 245-259. (pdf)
  83. F. Casas, J.A. Oteo and J. Ros. Floquet theory: exponential perturbation treatment. Journal of Physics A: Mathematical and General 34 (2001), 3379-3388. (pdf)
  84. S. Blanes, F. Casas and J. Ros. Processing symplectic methods for near-integrable Hamiltonian systems. Celestial Mechanics and Dynamical Astronomy 77 (2000), 17-36. (pdf)
  85. S. Blanes, F. Casas and J. Ros. Improved high order integrators based on the Magnus expansion. BIT 40 (2000), 434-450. (pdf)
  86. S. Blanes, F. Casas and J. Ros. Extrapolation of symplectic integrators. Celestial Mechanics and Dynamical Astronomy 75 (1999), 149-161. (pdf)
  87. S. Blanes, F. Casas and J. Ros. Symplectic integration with processing: a general study. SIAM Journal on Scientific Computing 21 (1999), 711-727. (pdf)
  88. S. Blanes, F. Casas, J.A. Oteo and J. Ros. Magnus and Fer expansions for matrix differential equations: the convergence problem. Journal of Physics A: Mathematical and General 31 (1998), 259-268. (pdf)
  89. F. Casas and C. Grebogi. Control of chaotic impacts. International Journal of Bifurcations and Chaos 7 (1997), 951-955. (pdf)
  90. F. Casas. Solution of linear partial differential equations by Lie algebraic methods. Journal of Computational and Applied Mathematics 76 (1996), 159-170. (pdf)
  91. F. Casas, W. Chin, C. Grebogi and E. Ott. Universal grazing bifurcations in impact oscillators. Physical Review E 53 (1996), 134-139. (pdf)
  92. F. Casas. Fer's factorization as a symplectic integrator. Numerische Mathematik 74 (1996), 283-303. (pdf)
  93. F. Casas, J.A. Oteo and J. Ros. Linear time-dependent Hamiltonian systems beyond the adiabatic limit. Journal of Physics A: Mathematical and General 27 (1994), 4325-4339. (pdf)
  94. F. Casas, J.A. Oteo and J. Ros. Variation of the action in the classical time-dependent harmonic oscillator: an exact result. Journal of Physics A: Mathematical and General 26 (1993), L315-L318. (pdf)
  95. F. Casas, J.A. Oteo and J. Ros. Geometric factors in the adiabatic evolution of classical systems. Physics Letters A 163 (1992), 359-363. (pdf)
  96. F. Casas, J.A. Oteo and J. Ros. Lie algebraic approach to Fer's expansion for classical Hamiltonian systems. Journal of Physics A: Mathematical and General 24 (1991), 4037-4046. (pdf)