Publications in Scientific Journals

  1. F. Casas, A. Murua, and M. Nadinic, Efficient computation of the Zassenhaus formula, Computer Physics Communications 183, 11, (2012), 2386-2391.
  2. 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.
  3. 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.
  4. S. Blanes, F. Casas, and A. Murua, Splitting methods in the numerical integration of non-autonomous dynamical systems, RACSAM. 106 (2012), 49-66.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. S. Blanes, F. Casas, and A. Murua, Splitting methods with complex coefficients, Bol. Soc. Esp. Mat. Apl. 50 (2010), 47-61.
  10. P. Chartier and A. Murua, An algebraic theory of order , M2AN 43 (2009) 607-630
  11. J. Makazaga, A. Murua, A new class of symplectic integration schemes based on generating functions , Numerische Mathematik, Vol. 113, Issue 4 (2009), 631--642
  12. 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)
  13. 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
  14. S. Blanes, F. Casas, A. Murua, On the linear stability of splitting methods , Found Comput Math 8 (2008), 357--393
  15. S. Blanes, F. Casas, A. Murua, Splitting methods for non-autonomous linear systems , Int. J. Comput. Math. 84(6) (2007), 713--727
  16. 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
  17. S. Blanes, F. Casas, A. Murua, Symplectic operator splitting methods for the time-dependent Schrödinger equation, Journal of Chemical Physics, vol. 124 (2006)
  18. 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
  19. A. Murua, The Hopf algebra of rooted trees, free Lie algebras, and Lie series, Foundations of Computational Mathematics, vol. 6 (2006), 387--426
  20. S. Blanes, F. Casas, A. Murua, Composition methods for differential equations with processing , SIAM Journal of Scientific Computing, vol. 27, No.6 (2005), 1817--1843
  21. 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
  22. 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
  23. J. Makazaga, A. Murua, New Runge-Kutta based schemes for ODEs with cheap global error estimation, Bit Numerical Mathematics, vol 43 (2003), 595-610
  24. 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
  25. R. Chan, A. Murua, Extrapolation of Symplectic methods for Hamiltonian problems, Applied Numerical Mathematics 34 (2000) 189-205
  26. J. Makazaga, A. Murua, Cheap one-step global error estimation for ODEs, New Zeland Journal of Mathematics 29 (2000), 211-221
  27. A. Murua, Formal Series and Numerical integrators. Part I: Systems of ODEs and symplectic Integrators, Applied Numerical Mathematics 29 (1999), 221-251
  28. A. Murua, Formal Series and Numerical integrators. Part II: Application to index 2 differential-algebraic systems, Applied Numerical Mathematics 29 (1999), 99-113
  29. 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
  30. 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
  31. M. Arnold, A. Murua, Non-stiff integrators for differential-algebraic systems of index 2, Numerical Algorithms 19 (1998), 25-41
  32. A. Murua, Order conditions for partitioned symplectic methods, SIAM Journal of Numerical Analysis, Vol 34, No. 6 (1997), 2204-2211
  33. 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
  34. A. Murua, Partitioned half-explicit Runge-Kutta methods for differential-algebraic systems of index 2, Computing, Vol 59, No 1 (1997), 43-61
  35. E. Hairer, A. Murua, and J. M. Sanz-Serna, The non-existence of symplectic multi-derivative Runge-Kutta methods, BIT 34 (1994), 80-87
  36. M. P. Calvo, A. Murua, and J. M. San z-Serna, Modified equations for ODEs, Contentemporary Mathematics, Vol 172, American Mathematical Society (1994), 63-74
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