Listar IMAC_Articles por autoría "31a75131-2879-4ab1-bbac-c669aa5c16b2"
Mostrando ítems 1-12 de 12
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Applying splitting methods with complex coefficients to the numerical integration of unitary problems
Blanes, Sergio; Casas, Fernando; Escorihuela-Tomàs, Alejandro American Institute of Mathematical Sciences (AIMS) (2022)We explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schr¨odinger equation. We prove that a particular class of integrators are conjugate to unitary ... -
Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation
Bader, Philipp; Blanes, Sergio; Casas, Fernando MDPI (2019)A new way to compute the Taylor polynomial of a matrix exponential is presented which reduces the number of matrix multiplications in comparison with the de-facto standard Paterson-Stockmeyer method for polynomial ... -
Computing the matrix sine and cosine simultaneously with a reduced number of products
Seydaoğlu, Muaz; Bader, Philipp; Blanes, Sergio; Casas, Fernando Elsevier (2021-05)A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two versions ... -
Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear evolution equations of parabolic type
Blanes, Sergio; Casas, Fernando; Thalhammer, Mechthild Oxford University Press (2018-04)The main objective of this work is to provide a stability and error analysis of high-order commutator-free quasi-Magnus (CFQM) exponential integrators. These time integration methods for nonautonomous linear evolution ... -
Efficient time integration methods for Gross-Pitaevskii equations with rotation term
Bader, Philipp; Blanes, Sergio; Casas, Fernando; Thalhammer, Mechthild American Institute of Mathematical Sciences (2019)The objective of this work is the introduction and investigation of favourable time integration methods for the Gross-Pitaevskii equation with rotation term. Employing a reformulation in rotating Lagrangian coordinates, ... -
Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type
Blanes, Sergio; Casas, Fernando; González, Cesáreo; Thalhammer, Mechthild Elsevier (2023-11-10)The present work is concerned with the extension of modified potential operator splitting methods to specific classes of nonlinear evolution equations. The considered partial differential equations of Schrödinger and ... -
Novel symplectic integrators for the Klein-Gordon equation with space- and time-dependent mass
Bader, Philipp; Blanes, Sergio; Casas, Fernando; Kopylov, Nikita Elsevier (2019-04)We consider the numerical time-integration of the non-stationary Klein–Gordon equation with position- and time-dependent mass. A novel class of time-averaged symplectic splitting methods involving double commutators is ... -
Preface for the special issue “Geometric numerical integration, twenty-five years later”
Blanes, Sergio; Casas, Fernando Taylor and Francis (2023) -
Runge–Kutta–Nyström symplectic splitting methods of order 8
Blanes, Sergio; Casas, Fernando; Escorihuela-Tomàs, Alejandro Elsevier (2022-12)Different families of Runge–Kutta–Nyström (RKN) symplectic splitting methods of order 8 are presented for second-order systems of ordinary differential equations and are tested on numerical examples. They show a better ... -
Splitting and composition methods in the numerical integration of differential equations
Blanes, Sergio; Murua, Ander; Casas, Fernando Sociedad Española de Matemática Aplicada (2008)We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field ... -
Splitting and composition methods with embedded error estimators
Blanes, Sergio; Casas, Fernando; Thalhammer, Mechthild Elsevier (2019-12)We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, ... -
Symplectic propagators for the Kepler problem with time-dependent mass
Bader, Philipp; Blanes, Sergio; Casas, Fernando; Kopylov, Nikita Springer (2019-06)New numerical integrators specifically designed for solving the two-body gravitational problem with a time-varying mass are presented. They can be seen as a generalization of commutator-free quasi-Magnus exponential ...