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Listar por palabra clave "Magnus expansion"

Mostrando ítems 1-8 de 8

Efficient numerical integration for N th-order non-autonomous linear differential equations

Bader, Philipp Karl Heinz; Blanes Zamora, Sergio; Casas, Fernando; Ponsoda Miralles, Enrique (Elsevier, 2016-01-01)

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 ...
Geometric Integrators for Schrödinger Equations

Bader, Philipp Karl-Heinz (Universitat Politècnica de València, 2014-07-11)

The celebrated Schrödinger equation is the key to understanding the dynamics of quantum mechanical particles and comes in a variety of forms. Its numerical solution poses numerous challenges, some of which are addressed ...
Magnus-based geometric integrators for dynamical systems with time-dependent potentials

Kopylov, Nikita (Universitat Politècnica de València, 2019-03-27)

[ES] Esta tesis trata sobre la integración numérica de sistemas hamiltonianos con potenciales explícitamente dependientes del tiempo. Los problemas de este tipo son comunes en la física matemática, porque provienen de la ...
Novel symplectic integrators for the Klein-Gordon equation with space- and time-dependent mass

Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando; Kopylov, Nikita (Elsevier, 2019-04)

[EN] 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 ...
Performance of fourth and sixth-order commutator-free Magnus expansion integrators for Ehrenfest dynamics

Gómez Pueyo, Adrián; Blanes Zamora, Sergio; Castro, Alberto (John Wiley & Sons, 2021)

[EN] Hybrid quantum-classical systems combine both classical and quantum degrees of freedom. Typically, in Chemistry, Molecular Physics, or Materials Science, the classical degrees of freedom describe atomic nuclei (or ...
Simulation of bimolecular reactions: Numerical challenges with the graph Laplacian

MacNamara, S.; Blanes Zamora, Sergio; Iserles, Arieh (Cambridge University Press, 2020-06-16)

[EN] An important framework for modelling and simulation of chemical reactions is a Markov process sometimes known as a master equation. Explicit solutions of master equations are rare; in general the explicit solution of ...
Symplectic integrators for second-order linear non-autonomous equations

Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando; Kopylov, Nikita; Ponsoda Miralles, Enrique (Elsevier, 2018)

[EN] 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 ...
Symplectic integrators for the matrix Hill equation

Bader, Philipp; Blanes Zamora, Sergio; Ponsoda Miralles, Enrique; Seydaoglu, Muaz (Elsevier, 2017)

[EN] We consider the numerical integration of the matrix Hill equation. Parametric resonances can appear and this property is of great interest in many different physical applications. Usually, Hill s equations originate ...