Publications

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2012

• [41] S. Blanes, F. Casas, P. Chartier, and A. Murua, Optimized high-order splitting methods for some classes of parabolic equations, Math. Comput. In Press. arXiv:1102.1622v1 [math.NA]
• [40] S. Blanes, F. Casas, and A. Murua, Splitting methods in the numerical integration of non-autonomous dynamical systems. RACSAM. 106 (2012), pp. 49-66. DOI: 10.1007/s13398-011-0024-8
• [39] S. Blanes and E. Ponsoda, Exponential integrators for non-homogeneous linear initial and boundary value problems. Applied Numerical Mathematics. In press. DOI: 10.1016/j.apnum.2012.02.001

2011

• [38] 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.
• [37] 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]
• [36] S. Blanes and E. Ponsoda, Magnus integrators for solving linear-quadratic differential games. Submitted.
• [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.

2010

• [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. Casas, and A. Murua, Splitting methods with complex coefficients. Bol. Soc. Esp. Mat. Apl. 50 (2010), pp. 47–61.
• [32] 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.

2009

• [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.

2008

• [30] S. Blanes, F. Casas, and A. Murua, Splitting and composition methods in the numerical integration of differential equations, Bol. Soc. Esp. Mat. Apl. 45 (2008), pp. 87–143.
• [29] S. Blanes, F. Casas and A. Murua, On the linear stability of splitting methods. Found. Comp. Math. 8 (2008), pp. 357-393.

2007

• [28] S. Blanes, F. Casas and A. Murua, Splitting methods for non-autonomous linear systems. International Journal of Computer Mathematics, 6 (2007), pp. 713-727 (Special Issue on Splitting Methods for Differential Equations.).

2006

• [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. Num. 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.

2005

• [22] S. Blanes and F. Casas, On the necessity of negative coefficients for operator splitting schemes of order higher than two. Appl. Num. 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.

2004

• [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.

2003

• [16] S. Blanes and F. Casas, Optimization of Lie-group methods, Future Gener. Comp. Sy., 19 (2003),pp. 331-339.

2002

• [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.

2001

• [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.

2000

• [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.

1999

• [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.

1998

• [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.

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