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Continuous changes of variables and the Magnus expansion
(IOP, 2019-09-23)
In this paper, we are concerned with a formulation of Magnus and Floquet-Magnus expansions for general nonlinear differential equations. To this aim, we introduce suitable continuous variable transformations generated by ...
Splitting and composition methods with embedded error estimators
(Elsevier, 2019-12)
We propose new local error estimators for splitting and composition methods. They are based on the construction of lower order schemes obtained at each step as a linear combination of the intermediate stages of the integrator, ...
Runge–Kutta–Nyström symplectic splitting methods of order 8
(Elsevier, 2022-12)
Different families of Runge–Kutta–Nyström (RKN) symplectic splitting methods of order 8 are presented for second-order systems of ordinary differential equations and are tested on numerical examples. They show a better ...
Applying splitting methods with complex coefficients to the numerical integration of unitary problems
(American Institute of Mathematical Sciences (AIMS), 2022)
We explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schr¨odinger equation.
We prove that a particular class of integrators are conjugate to unitary ...
Symplectic propagators for the Kepler problem with time-dependent mass
(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 ...
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 ...
A Unifying Framework for Perturbative Exponential Factorizations
(MDPI, 2021-03-17)
We propose a framework where Fer and Wilcox expansions for the solution of differential
equations are derived from two particular choices for the initial transformation that seeds the product
expansion. In this scheme, ...
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 ...
A general formula for the Magnus expansion in terms of iterated integrals of right-nested commutators
(IOP, 2018-03)
We present a general expression for any term of the Magnus series as an iterated integral of a linear combination of independent right-nested commutators with given coefficients. The relation with the Malvenuto–Reutenauer ...