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Exponential Perturbative Expansions and Coordinate Transformations
(MDPI, 2020)
We propose a unified approach for different exponential perturbation techniques used in
the treatment of time-dependent quantum mechanical problems, namely the Magnus expansion,
the Floquet–Magnus expansion for periodic ...
The Lie-group method based on radial basis functions for solving nonlinear high dimensional generalized Benjamin–Bona–Mahony–Burgers equation in arbitrary domains
(Elsevier, 2018-03-15)
The aim of this paper is to introduce a new numerical method for solving the nonlinear generalized Benjamin–Bona–Mahony–Burgers (GBBMB) equation. This method is combination of group preserving scheme (GPS) with radial basis ...
A note on the Baker–Campbell–Hausdorff series in terms of right-nested commutators
(Springer, 2021-01-27)
We get compact expressions for the Baker–Campbell–Hausdorff
series Z = log(eX eY ) in terms of right-nested commutators. The reduction in the number of terms originates from two facts: (i) we use as a
starting point an ...
Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation
(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 ...
Numerical integrators based on the Magnus expansion for nonlinear dynamical systems
(Elsevier, 2020-03-15)
Explicit numerical integration algorithms up to order four based on the Magnus expansion for nonlinear non-autonomous ordinary differential equations are presented and tested on problems possessing qualitative (very often, ...
Efficient time integration methods for Gross-Pitaevskii equations with rotation term
(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, ...
Novel symplectic integrators for the Klein-Gordon equation with space- and time-dependent mass
(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 ...
Splitting and composition methods in the numerical integration of differential equations
(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 ...
Generalisation of splitting methods based on modified potentials to nonlinear evolution equations of parabolic and Schrödinger type
(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 order integrators obtained by linear combinations of symmetric-conjugate compositions
(Elsevier, 2022-02-01)
A new family of methods involving complex coefficients for the numerical integration of differential equations is presented and analyzed. They are constructed as linear combinations of symmetric-conjugate compositions ...