85 citations · 245 across the 20 of their papers we have counts for
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An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrödinger equation
Philipp Bader, Sergio Blanes, Fernando Casas +1
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 matri…
Computing the matrix sine and cosine simultaneously with a reduced number of products
Muaz Seydaoglu, Philipp Bader, Sergio Blanes +1
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 o…
Efficient time integration methods for Gross--Pitaevskii equations with rotation term
Philipp Bader, Sergio Blanes, Fernando Casas +1
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 reformula…
Exponential propagators for the Schrödinger equation with a time-dependent potential
Philipp Bader, Sergio Blanes, Nikita Kopylov
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. Commutato…
An improved algorithm to compute the exponential of a matrix
Philipp Bader, Sergio Blanes, Fernando Casas
In this work, we present a new way to compute the Taylor polynomial of the matrix exponential which reduces the number of matrix multiplications in comparison with the de-facto sta…
Symplectic integrators for second-order linear non-autonomous equations
Philipp Bader, Sergio Blanes, Fernando Casas +2
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…