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· [2] E.S. Carlin, S. Blanes, F. Casas, Reformulating polarized
radiative transfer.(I) A consistent formalism allowing non-local Magnus
solutions, arXiv preprint arXiv:2402.00252
· [3] S. Blanes, Parallel Computation of functions of
matrices and their action on vectors for exponential integrators. Submitted.
· [91] V.J. Bevia, S. Blanes, J.C.
Cortés, N. Kopylov, R.J. Villanueva, A GPU-accelerated Lagrangian method
for solving the Liouville equation in random differential equation systems, Appl. Numer. Math. In press
· [90] S. Blanes, N. Kopylov and M Seydaoğlu, Efficient scaling and squaring
method for the matrix exponential, SIAM J. Matr. Anal. Appl. In press. arXiv:submit/5546993.
· [89] S. Blanes, F. Casas, A. Escorihuela-Tomŕs, Families of efficient low order processed composition methods, Appl. Numer. Math., 204 (2024),
pp. 86-100. arXiv:2404.04340
· [88] S. Blanes, F. Casas, and A. Murua, Splitting Methods for differential equations, Acta Numerica (2024), pp. 1-161.
· [87] S. Blanes, F. Casas, L. Shaw, Generalized extrapolation methods based on compositions of a basic
2nd-order scheme, Applied Mathematics and Computation 473 (2024), 128663
· [86] S. Blanes, F. Casas, C. González, M. Thalhammer, Symmetric-conjugate splitting
methods for evolution equations of parabolic type, Journal of Computational Dynamics, 11 ( 2024), pp. 108-134
· [85] S. Blanes, F. Casas, C. González, 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.
2023
· [84] S. Blanes, F. Casas, C.
González, M. Thalhammer, Efficient Splitting Methods Based on
Modified Potentials: Numerical Integration of Linear Parabolic Problems and
Imaginary Time Propagation of the Schrodinger Equation, Commun. Comput. Phys. 33, No. 4,
(2023), pp. 937-961
· [83] J Bernier, S. Blanes, F. Casas, and A.
Escorihuela-Tomŕs, Symmetric-conjugate splitting methods for linear unitary problems, BIT Numerical Mathematics (2023)
63:58
· [82] S. Blanes, A. Iserles and S. MacNamara, Positivity-preserving methods for ordinary
differential equations. ESAIM: Mathematical Modelling and
Numerical Analysis 56 (2022), 1843-1870.
· [81] S. Blanes, F. Casas and A. Escorihuela-Tomŕs, Runge-Kutta-Nyström symplectic splitting methods of order 8. Applied Numerical Mathematics 182 (2022), 14-27.
· [80] 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.
· [79] S. Blanes, F. Casas and A. Escorihuela-Tomŕs, Applying splitting methods with complex
coefficients to the numerical integration of unitary problems, J. Comput. Dyn. 9 (2022), 85-101.
· [78] P. Bader, S. Blanes, F. Casas and M Seydaoğlu, An efficient algorithm to compute
the exponential of skew-Hermitian matrices for the time integration of the
Schrödinger equation, Math. Comput. Sim. 194 (2022), pp. 383-400.
· [77] S. Blanes, Novel parallel in time integrators for ODEs, Applied Mathematics Letters, 122 (2021) 107542.
· [76] S. Blanes, M.P. Calvo, F. Casas and J.M. Sanz-Serna, Symmetrically processed splitting
integrators for enhanced Hamiltonian Monte Carlo sampling, SIAM J. Sci. Comput. 43 (2021), pp. A3357-A3371.
· [75] M. Seydaoğlu, P. Bader, S. Blanes and F. Casas, Computing the matrix sine and cosine
simultaneously with a reduced number of products, Appl. Num. Math., 163
(2021), 96-107.
· [74] 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 J. Numer. Anal. 41 (2021), pp. 594–617.
· [73] A. Gómez_Pueyo, S. Blanes and A. Castro, Performance of fourth and sixth‐order
commutator‐free Magnus expansion integrators for Ehrenfest dynamics, Computational and Mathematical
Methods 3 (2021), e1100.
· [72] S. Blanes, S. MacNamara and A. Iserles, Simulation of bimolecular reactions:
numerical challenges with the graph Laplacian, ANZIAM J. 61 (EMAC2019)
(2020), pp. C1-C16.
· [71] A. Gómez_Pueyo, S. Blanes and A. Castro, Propagators for Quantum-Classical
Models: Commutator-Free Magnus Methods, Journal of Chemical Theory and
Computation 16 (2020), pp. 1420-1430.
· [70] S. Blanes, V. Gradinaru, High order efficient splittings for
the semiclassical time–dependent Schrödinger equation, J Comput. Phys. 405 (2020) 109157.
· [69] P. Bader, S. Blanes, F. Casas and M. Thalhammer, Efficient time integration methods
for Gross--Pitaevskii equations with rotation term, J. Comput. Dyn. 6 (2019),
147-169.
· [68] P. Bader, S. Blanes and F: Casas, Computing the matrix exponential
with an optimized Taylor polynomial approximation, Mathematics 7 (2019), 1174.
· [67] S. Blanes, F. Casas, and M. Thalhammer, Splitting and composition methods with embedded
error estimators. Appl. Numer. Math. 146 (2019),
pp. 400-415. arXiv:1903.05391v1 [math.NA]
· [66] S. Blanes, On the construction of symmetric second order methods for ODEs, Applied Mathematics Letters, 98 (2019), pp. 41-48.
· [65] P. Bader, S. Blanes, F: Casas, and N. Kopylov, Symplectic propagators for the
Kepler problem with time-dependent mass, Celest. Mech. & Dyn. Astron. 131:25
(2019), pp.1-19.
· [64] P. Bader, S. Blanes, F: Casas, and N. Kopylov, Novel symplectic integrators for the
Klein-Gordon equation with space- and time-dependent mass, J. Comput. Appl. Math. 350
(2019), pp. 130-138.
· [63] P. Bader, S. Blanes, and N.
Kopylov, Exponential propagators for the
Schrödinger equation with a time-dependent potential, J. Chem. Phys. 148, 244109
(2018). arXiv:1804.07103 [math.NA].
· [62] S. Blanes, Time-average
on the numerical integration of non-autonomous differential equations, SIAM
J. Numer. Anal. 56
(2018), pp. 2513-2536.
· [61] 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 J. Numer. Anal. 38
(2018), pp. 743–778. doi: 10.1093/imanum/drx012.
· [60] P. Bader, S. Blanes, F: Casas, N. Kopylov,
and E. Ponsoda, Symplectic integrators for second-order linear
non-autonomous equations. J. Comput. Appl. Math. 330 (2018), pp. 909-919. arXiv: 1702.04768 [math.NA].
· [59] S. Blanes, F. Casas, and M.
Thalhammer, High-order commutator-free quasi-Magnus
exponential integrators for non-autonomous linear evolution equations. Comput. Phys. Comm. 220 (2017),
243-262.
· [58] S. Blanes, F. Casas, and A. Murua, Symplectic
time-average propagators for the Schödinger equation with a time-dependent
Hamiltonian, J. Chem. Phys. 146, 114109 (2017).
· [57] P. Bader, S. Blanes, E. Ponsoda, and M
Seydaoglu, Symplectic integrators for the matrix Hill's
equation and its applications to engineering models. J. Comput. Appl.
Math., 316 (2017), pp. 47-59. arXiv:1512.02343 [math.NA].
· [56] P. Bader, S. Blanes, F. Casas,
and E. Ponsoda, Efficient Numerical Integration of
Nth-order non-Autonomous Linear Differential Equations. J. Comput. Appl.
Math., 291 (2016), pp. 380-390.
· [55] 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)
· [54] S. Blanes, Explicit
symplectic RKN methods for perturbed non-autonomous oscillators: splitting,
extended and exponentially fitting methods. Comput. Phys. Comm., 195
(2015), pp. 10-18.
· [53] P. Bader, S. Blanes, and M
Seydaoglu, The
Scaling, Splitting and Squaring Method for the Exponential of Perturbed
Matrices. SIAM J. Matrix Anal., 36 (2015), pp. 549-614.
· [52] S. Blanes, High
order structure preserving explicit methods for solving linear-quadratic
optimal control problems. Numerical Algorithms, 69 (2015), pp.
271-290.
· [51] S. Blanes, F. Casas, J.A. Oteo
and J. Ros, The Fer and Magnus expansions. Encyclopedia of Applied
and Computational Mathematics, Springer. Engquist, Björn (Ed.) (2015).
· [50] S. Blanes, F. Casas, and A.
Murua, Splitting methods. Encyclopedia
of Applied and Computational Mathematics, Springer. Engquist, Björn (Ed.) (2015).
· [49] M Seydaoglu and S. Blanes, High-order splitting methods for separable non-autonomous
parabolic equations. Appl. Numer. Math., 84 (2014), pp. 22-32.
· [48] S. Blanes, F. Casas and J.M.
Sanz-Serna, Numerical integrators for the Hybrid Monte
Carlo method. SIAM
J. Sci. Comput. 36 (2014), pp. A1556-A1580.
· [47] S. Blanes and E. Ponsoda, Exponential integrators for coupled self-adjoint
non-autonomous partial differential equations. Appl. Math. Comput., 243
(2014), pp. 1-11.
· [46] P. Bader, S. Blanes, and E.
Ponsoda, Structure preserving integrators for solving
linear quadratic optimal control problems with applications to describe the
flight of a quadrotor. J. Comput. Appl. Math., 262 (2014), pp.
223-233. arXiv:1212.0474v1
· [45] P. Bader, S. Blanes, and F.
Casas, Solving the Schrödinger eigenvalue problem by the imaginary time
propagation technique using splitting methods with complex coefficients. J. Chem. Phys. 139, 124117
(2013). arXiv:1304.6845
· [44] A. Farrés, J. Laskar, S.
Blanes, F. Casas, J. Makazaga, and A. Murua, High
precision Symplectic Integrators for the Solar System. Celest. Mech. & Dyn. Astron., 116
(2013), pp. 141-174. arXiv:1208.0716v1
· [43] 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 (Fortran programs)
· [42] 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. arXiv:1102.1622v1 [math.NA]
· [41] S. Blanes and A. Iserles, Explicit Adaptive Symplectic Integrators for solving
Hamiltonian Systems, Celest. Mech. & Dyn. Astron. 114 (2012), pp. 297-317.
· [40] S. Blanes and E. Ponsoda, Magnus integrators for solving linear-quadratic
differential games. J. Comput. Appl. Math. 236 (2012), pp.
3394-3408.
· [39] S. Blanes, F. Casas, and A.
Murua, Splitting methods in the numerical integration
of non-autonomous dynamical systems. RACSAM. 106 (2012), pp. 49-66.
· [38] S. Blanes and E. Ponsoda, Time-averaging
and exponential integrators for non-homogeneous linear IVPs and BVPs. Appl. Numer. Math. 62
(2012), pp. 875-894.
· [37] E. Ponsoda, S. Blanes and P. Bader, New efficient numerical methods to describe the heat transfer in a solid medium, Math. Comp. Mod. 54 (2011), pp. 1858-1862.
· [36] P. Bader and S. Blanes, Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schrödinger equations. Phys. Rev. E. 83, 046711 (2011). arXiv:1007.3470v2 [math.NA]
· [35] S. Blanes, F. Casas, and A. Murua, Error analysis of splitting methods for the time dependent Schrodinger equation, SIAM J. Sci. Comput. 33 (2011), pp. 1525-1548.
·
[34] S. Blanes, F. Casas, J.A. Oteo and J. Ros, A
pedagogical approach to the Magnus expansion, Eur. J. Phys., 31
(2010), pp. 907-918.
· [33] S. Blanes, F. Diele, C. Marangi, and S. Ragni, Splitting and composition methods for explicit time dependence in separable dynamical systems. J. Comput. Appl. Math., 235 (2010), pp. 646-659.
· [32] S. Blanes, F. Casas, and A. Murua, Splitting methods with complex coefficients. Bol. Soc. Esp. Mat. Apl. 50 (2010), pp. 47–61.
· [31] S. Blanes, F. Casas, J.A. Oteo and J. Ros, The Magnus and expansion and some of its applications. Physics Reports, 470 (2009), pp. 151-238.
· [30] S. Blanes, F. Casas and A. Murua, On the linear stability of splitting methods. Found. Comp. Math. 8 (2008), pp. 357-393.
· [29] S. Blanes, F. Casas, and A. Murua, Splitting and composition methods in the numerical integration of differential equations, Bol. Soc. Esp. Mat. Apl. (SEMA) 45 (2008), pp. 87–143.
·
[28]
S. Blanes, F. Casas and A. Murua, Splitting methods for
non-autonomous linear systems. Int. J. Computer Math., 6 (2007), pp. 713-727 (Special Issue on
Splitting Methods for Differential Equations.).
· [27] S. Blanes, F. Casas and A. Murua, Symplectic splitting operator methods for the time-dependent Schrödinger equation. J. Chem. Phys. 124 (2006) 234105.
· [26] S. Blanes and F. Casas, Comment on `Structure of positive decomposition of exponential operators' . Phys. Rev. E. 73 (2006) 048701.
·
[25]
S. Blanes and F. Casas, Splitting methods for
non-autonomous separable dynamical system. J. Phys. A: Math. Gen. 39 (2006), pp.
5405-5423. (Special issue on Geometric Numerical Integration).
· [24] S. Blanes and P.C. Moan, Fourth- and sixth-order commutator-free Magnus integrators for linear and non-linear dynamical systems. Appl. Numer. Math. 56 (2006), pp. 1519-1537.
· [23] S. Blanes, F. Casas and A. Murua, Composition methods for differential equations with processing . SIAM J. Sci. Comp. 27 (2006), pp. 1817-1843.
· [22] S. Blanes and F. Casas, On the necessity of negative coefficients for operator splitting schemes of order higher than two. Appl. Numer. Math. 54 (2005), pp. 23-37.
· [21] S. Blanes and C. J. Budd, Adaptive geometric integrators for Hamiltonian problems with approximate scale invariance, SIAM J. Sci. Comp. 26 (2005), pp. 1089-1113.
·
[20]
S. Blanes and F. Casas, Raising the order of geometric
numerical integrators by composition and extrapolation, Numerical Algorithms, 38
(2005), pp. 305-326.
· [19] S. Blanes and C. J. Budd, Explicit Adaptive SYmplectic (EASY) integrators: A scaling invariant generalisation of the Levi-Civita and KS regularisations, Celest. Mech. & Dyn. Astron., 89 (2004), pp. 383-405.
·
[18]
S. Blanes and F. Casas, On the convergence and
optimization of the Baker-Campbell-Hausdorff formula, Linear Algebra Appl., 378
(2004), pp. 135-158.
· [17] S. Blanes, F. Casas and A. Murua, On the numerical integration of ordinary differential equations by processed methods, SIAM J. Numer. Anal., 42 (2004), pp. 531-552.
· [16] S. Blanes and F. Casas, Optimization of Lie-group methods, Future Gener. Comp. Sy., 19 (2003),pp. 331-339.
· [15] S. Blanes, Symplectic Maps for Approximating Polynomial Hamiltonian Systems, Phys. Rev. E., 65 (2002) 056703.
·
[14]
S. Blanes, F. Casas and J. Ros, High order optimized
geometric integrators for linear differential equations, BIT, 42
(2002), pp. 262-284.
· [13] S. Blanes and P.C. Moan, Practical Symplectic Partitioned Runge-Kutta and Runge-Kutta-Nyström Methods, J. Comput. Appl. Math., 142 (2002), pp. 313-330.
· [12] S. Blanes and P.C. Moan, Splitting Methods for non-autonomous differential equations, J. Comput. Phys., 170 (2001), pp. 205-230.
· [11] S. Blanes, High Order Numerical Integrators for Differential Equations using Composition and Processing of low Order Methods, Appl. Num. Math., 37 (2001), pp. 289-306.
· [10] S. Blanes, F. Casas and J. Ros, New families of symplectic Runge-Kutta-Nyström integration methods, Lecture Notes in Computer Science. L. Vulkov, J. Wasniewski, and Yalamov (Eds.): NAA 2000, LNCS 1988, pp. 102-109, 2001. Springer-Verlag Berlin Heidelberg 2001.
· [9] S. Blanes, F. Casas and J. Ros, High-order Runge-Kutta-Nyström geometric methods with processing , Appl. Num. Math., 39 (2001), pp. 245-259.
· [8] S. Blanes, F. Casas, and J. Ros, Processing symplectic methods for near-integrable Hamiltonian systems, Celest. Mech. & Dyn. Astron., 77 (2000), pp. 17-36.
·
[7]
S. Blanes, F. Casas and J. Ros, Improved high order integrators
based on Magnus expansion, BIT, 40 (2000), pp. 434-450.
· [6] S. Blanes and P.C. Moan, Splitting methods for the time-dependent Schrödinger equation, Phys. Lett. A, 265, (2000), pp. 35-42.
· [5] S. Blanes, L. Jodar and E. Ponsoda, Approximate solutions with a priori error bounds for continuous coefficient matrix Riccati equations , Math. Comp. Modelling, 31 (2000), pp. 1-15.
· [4] S. Blanes, F. Casas, and J. Ros, Extrapolation of symplectic integrators; Celest. Mech. & Dyn. Astron., 75 (1999), pp. 149-161.
·
[3]
S. Blanes, F. Casas and J. Ros, Symplectic integration with
processing: A general study, SIAM J. Sci., Comp. 21 (1999), pp. 711-727.
· [2] S. Blanes and L. Jodar, Continuous numerical solutions of coupled mixed partial differential systems using Fer's factorization, J. Comp. Appl. Math., 101 (1999), pp. 189-202.
· [1] S. Blanes, F. Casas, J.A. Oteo and J. Ros, Magnus and Fer expansions for matrix differential equations: the convergence problem, J. Phys. A: Math. Gen., 31 (1998), pp. 259-268.
· [5] P. Bader
and S. Blanes, Solving the pertubed quantum harmonic oscillator in imaginary
time using splitting methods with complex coefficients. Springer International
Publishing Switzerland 2014 F. Casas, V. Martinez (eds.), Advances in
Differential Equations and Applications, SEMA SIMAI Springer Series 4, DOI
10.1007/978-3-319-06953-1_21
· [4] S. Blanes and M. Seydaoglu, Splitting methods with real-complex coefficients for separable non-autonomous semi-linear reaction-diffusion equation of Fisher. Proceedings del XXIII Congreso de Ecuaciones Diferenciales y Aplicaciones XIII Congreso de Matemática Aplicada Castellón, 9-13 septiembre 2013.
· [3] S. Blanes, F. Casas and J.M. Sanz-Serna, Beating
the Verlet integrator in Monte Carlo simulations. AIP Conf. Proceedings 1558,
(2013); pp. 8-10. doi: 10.1063/1.4825407
· [2] S. Blanes, F. Casas, and A. Murua, Splitting and composition methods for the time dependent Schrödinger equation. Mathematisches Forschungsinstitut Oberwolfach, Geometric Numerical Integration, Report No. 16/2011.
· [1] S. Blanes, F. Casas, and A. Murua, Splitting methods in Geometric Numerical Integration. Mathematisches Forschungsinstitut Oberwolfach, Geometric Numerical Integration, Report No. 14/2006.