Splitting and composition methods in the numerical integration of differential equations S Blanes, F Casas, A Murua arXiv preprint arXiv:0812.0377, 2008 | 167 | 2008 |
Efficient computation of the Zassenhaus formula F Casas, A Murua, M Nadinic Computer Physics Communications 183 (11), 2386-2391, 2012 | 149 | 2012 |
An algebraic approach to invariant preserving integators: the case of quadratic and Hamiltonian invariants P Chartier, E Faou, A Murua Numerische Mathematik 103, 575-590, 2006 | 142 | 2006 |
The Hopf algebra of rooted trees, free Lie algebras, and Lie series A Murua Foundations of Computational Mathematics 6 (4), 387-426, 2006 | 119 | 2006 |
An efficient algorithm for computing the Baker–Campbell–Hausdorff series and some of its applications F Casas, A Murua Journal of Mathematical Physics 50 (3), 2009 | 116 | 2009 |
New families of symplectic splitting methods for numerical integration in dynamical astronomy S Blanes, F Casas, A Farres, J Laskar, J Makazaga, A Murua Applied Numerical Mathematics 68, 58-72, 2013 | 110 | 2013 |
Order conditions for numerical integrators obtained by composing simpler integrators A Murua, JM Sanz–Serna Philosophical Transactions of the Royal Society of London. Series A …, 1999 | 101 | 1999 |
Symplectic methods based on decompositions AL Araújo, A Murua, JM Sanz-Serna SIAM journal on numerical analysis 34 (5), 1926-1947, 1997 | 84 | 1997 |
Optimized high-order splitting methods for some classes of parabolic equations S Blanes, F Casas, P Chartier, A Murua Mathematics of Computation 82 (283), 1559-1576, 2013 | 79 | 2013 |
High precision symplectic integrators for the solar system A Farrés, J Laskar, S Blanes, F Casas, J Makazaga, A Murua Celestial Mechanics and Dynamical Astronomy 116 (2), 141-174, 2013 | 69 | 2013 |
Higher-order averaging, formal series and numerical integration I: B-series P Chartier, A Murua, JM Sanz-Serna Foundations of Computational Mathematics 10 (6), 695-727, 2010 | 68 | 2010 |
Symplectic splitting operator methods for the time-dependent Schrödinger equation S Blanes, F Casas, A Murua The Journal of chemical physics 124 (23), 2006 | 68 | 2006 |
Modified equations for ODEs MP Calvo, A Murua, JM Sanz-Serna Contemporary Mathematics 172, 63-63, 1994 | 64 | 1994 |
Formal series and numerical integrators, Part I: Systems of ODEs and symplectic integrators A Murua Applied numerical mathematics 29 (2), 221-251, 1999 | 60 | 1999 |
Preserving first integrals and volume forms of additively split systems P Chartier, A Murua IMA journal of numerical analysis 27 (2), 381-405, 2007 | 54 | 2007 |
Higher-order averaging, formal series and numerical integration II: the quasi-periodic case P Chartier, A Murua, JM Sanz-Serna Foundations of Computational Mathematics 12, 471-508, 2012 | 46 | 2012 |
A formal series approach to averaging: exponentially small error estimates P Chartier, A Murua, JM Sanz-Serna Discrete and Continuous Dynamical Systems-Series A 32 (9), 2012 | 41 | 2012 |
Higher-order averaging, formal series and numerical integration III: error bounds P Chartier, A Murua, JM Sanz-Serna Foundations of Computational Mathematics 15, 591-612, 2015 | 40 | 2015 |
Numerical stroboscopic averaging for ODEs and DAEs MP Calvo, P Chartier, A Murua, JM Sanz-Serna Applied numerical mathematics 61 (10), 1077-1095, 2011 | 40 | 2011 |
Stroboscopic averaging for the nonlinear Schrödinger equation F Castella, P Chartier, F Méhats, A Murua Foundations of Computational Mathematics 15 (2), 519-559, 2015 | 39 | 2015 |