Listar por autoría "3bcbba22-bc6e-40f0-8ea1-9d1008a715f7"
Mostrando ítems 1-11 de 11
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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. ... -
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 ... -
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 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, ... -
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 ... -
Fourier-splitting methods for the dynamics of rotating Bose-Einstein condensates
Bader, Philipp Elsevier (2018-01)We present a new method to propagate rotating Bose–Einstein condensates subject to explicitly time-dependent trapping potentials. Using algebraic techniques, we combine Magnus expansions and splitting methods to yield any ... -
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 ... -
Solving the Schrödinger eigenvalue problem by the imaginary time propagation technique using splitting methods with complex
Bader, Philipp; Blanes, Sergio; Casas, Fernando American Institute of Physics (AIP Publishing LLC) (2013)The Schrödinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional ... -
Symplectic integrators for second-order linear non-autonomous equations
Bader, Philipp; Blanes, Sergio; Casas, Fernando; Kopylov, Nikita; Ponsoda, Enrique Elsevier (2018-03)Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they ... -
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 ...