Browsing Departament: Matemàtiques by Author "3bcbba22-bc6e-40f0-8ea1-9d1008a715f7"
Now showing items 1-8 of 8
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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 ... -
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 ... -
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 ...