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Composition Methods for Dynamical Systems Separable into Three Parts
(MDPI, 2020)
New families of fourth-order composition methods for the numerical integration of initial
value problems defined by ordinary differential equations are proposed. They are designed when
the problem can be separated into ...
Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear evolution equations of parabolic type
(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 ...
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 ...
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 ...
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 ...
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 ...
Computing the matrix sine and cosine simultaneously with a reduced number of products
(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 ...
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 ...
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 ...
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 ...