Listar por autoría "31a75131-2879-4ab1-bbac-c669aa5c16b2"
Mostrando ítems 1-20 de 34
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A pedagogical approach to the Magnus expansion
Blanes, Sergio; Casas, Fernando; Oteo, J. A.; Ros, J. Institute of Physics (2010-07)Time-dependent perturbation theory as a tool to compute approximate solutions of the Schrödinger equation does not preserve unitarity. Here we present, in a simple way, how the Magnus expansion (also known as exponential ... -
An efficient algorithm based on splitting for the time integration of the Schrödinger equation
Blanes, Sergio; Casas, Fernando; Murua, Ander Elsevier (2015-12)We present a practical algorithm based on symplectic splitting methods intended for the numerical integration in time of the Schrödinger equation when the Hamiltonian operator is either time-independent or changes slowly ... -
An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrödinger equation
Bader, Philipp; Blanes, Sergio; Casas, Fernando; Seydaoğlu, Muaz Elsevier B.V. (2022-04-30)We present a practical algorithm to approximate the exponential of skew-Hermitian matrices up to round-off error based on an efficient computation of Chebyshev polynomials of matrices and the corresponding error analysis. ... -
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 ... -
Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear Schrödinger equations
Blanes, Sergio; Casas, Fernando; González, Cesáreo; Thalhammer, Mechthild Oxford University Press (2020-03-02)This work is devoted to the derivation of a convergence result for high-order commutator-free quasi-Magnus (CFQM) exponential integrators applied to nonautonomous linear Schrödinger equations; a detailed stability and local ... -
Efficient numerical integration of NNth-order non-autonomous linear differential equations
Bader, Philipp; Blanes, Sergio; Casas, Fernando; Ponsoda, Enrique Elsevier (2016)We consider the numerical integration of high-order linear non-homogeneous differential equations, written as first order homogeneous linear equations, and using exponential methods. Integrators like Magnus expansions or ... -
Efficient Splitting Methods Based on Modified Potentials: Numerical Integration of Linear Parabolic Problems and Imaginary Time Propagation of the Schrodinger Equation
Blanes, Sergio; Casas, Fernando; González, Cesáreo; Thalhammer, Mechthild Global-Science Press (2023-05)We present a new family of fourth-order splitting methods with positive coefficients especially tailored for the time integration of linear parabolic problems and, in particular, for the time dependent Schrödinger equation, ... -
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, ... -
Error analysis of splitting methods for the time dependent Schrödinger equation
Blanes, Sergio; Casas, Fernando; Murua, Ander Society for Industrial and Applied Mathematics (2011)A typical procedure to integrate numerically the time dependent Schrödinger equation involves two stages. In the first stage one carries out a space discretization of the continuous problem. This results in the linear ... -
Exponential propagators for the Schrodinger equation with a time-dependent potential
Bader, Philipp; Blanes, Sergio; Kopylov, Nikita AIP Publishing (2018-06)We consider the numerical integration of the Schrödinger equation with a time-dependent Hamiltonian given as the sum of the kinetic energy and a time-dependent potential. Commutator-free (CF) propagators are exponential ... -
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 ... -
High precision Symplectic Integrators for the Solar System
Farrés Basiana, Ariadna; Laskar, Jacques; Blanes, Sergio; Casas, Fernando; Makazaga, Joseba; Murua, Ander Springer Netherlands (2013-02)Using a Newtonian model of the Solar System with all 8 planets, we perform extensive tests on various symplectic integrators of high orders, searching for the best splitting scheme for long term studies in the Solar System. ... -
High-order commutator-free quasi-Magnus exponential integrators for non-autonomous linear evolution equation
Blanes, Sergio; Casas, Fernando; Thalhammer, Mechthild Elsevier (2017-11)The class of commutator-free quasi-Magnus (CFQM) exponential integrators provides a favourable alternative to standard Magnus integrators, in particular for large-scale applications arising in the time integration of ... -
New families of symplectic splitting methods for numerical integration in dynamical astronomy
Blanes, Sergio; Casas, Fernando; Farrés Basiana, Ariadna; Laskar, Jacques; Makazaga, Joseba; Murua, Ander Elsevier (2013-06)We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interested in very accurate results over a large ... -
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 ... -
Numerical Integrators for the Hybrid Monte Carlo Method
Blanes, Sergio; Casas, Fernando; Sanz-Serna, JM Society for Industrial and Applied Mathematics (2014-05)We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the ... -
On the Linear Stability of Splitting Methods
Blanes, Sergio; Casas, Fernando; Murua, Ander Springer Verlag (2008)A comprehensive linear stability analysis of splitting methods is carried out by means of a 2 × 2 matrix K(x) with polynomial entries (the stability matrix) and the stability polynomial p(x) (the trace of K(x) divided by ...