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Listar por palabra clave "Splitting methods"

Mostrando ítems 1-13 de 13

Applying Splitting Methods With Complex Coefficients To The Numerical Integration Of Unitary Problems

Blanes Zamora, Sergio; Casas, Fernando; Escorihuela-Tomàs, Alejandro (American Institute of Mathematical Sciences, 2022-04)

[EN] We explore the applicability of splitting methods involving complex coefficients to solve numerically the time-dependent Schriidinger equation. We prove that a particular class of integrators are conjugate to unitary ...
Explicit symplectic RKN methods for perturbed non-autonomous oscillators: Splitting, extended and exponentially fitting methods

Blanes Zamora, Sergio (Elsevier, 2015-08)

We consider the numerical integration of perturbed non-autonomous oscillatory systems using high order methods. The autonomous case has been efficiently integrated using explicit and symplectic Runge–Kutta–Nyström (RKN) ...
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 ...
High order structure preserving explicit methods for solving linear-quadratic optimal control problems

Blanes Zamora, Sergio (Springer-Verlag, 2015)

[EN] We consider the numerical integration of linear-quadratic optimal control problems. This problem requires the solution of a boundary value problem: a non-autonomous matrix Riccati differential equation (RDE) with final ...
High-order splitting methods for separable non-autonomous parabolic equations

Seydaoglu, Muaz; Blanes Zamora, Sergio (Elsevier, 2014-10)

We consider the numerical integration of non-autonomous separable parabolic equations using high order splitting methods with complex coefficients (methods with real coeffi- cients of order greater than two necessarily ...
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 ...
New families of symplectic splitting methods for numerical integration in dynamical astronomy

Blanes Zamora, Sergio; Casas Perez, Fernando; Farrés, Ariadna; Laskar, Jacques; Makazaga, Joseba; Murua, Ander (Elsevier, 2013-06)

[EN] We present new splitting methods designed for the numerical integration of near-integrable Hamiltonian systems, and in particular for planetary N-body problems, when one is interested in very accurate results over a ...
Optimized High-Order Splitting Methods For Some Classes Of Parabolic Equations

Blanes Zamora, Sergio; Casas Perez, Fernando; Chartier, P.; Murua, A. (American Mathematical Society, 2013-07)

We are concerned with the numerical solution obtained by splitting methods of certain parabolic partial differential equations. Splitting schemes of order higher than two with real coefficients necessarily involve negative ...
Splitting and composition methods with embedded error estimators

Blanes Zamora, Sergio; Casas, Fernando; Thalhammer, Mechthild (Elsevier, 2019-12)

[EN] 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 ...
Splitting methods for differential equations

Blanes Zamora, Sergio; Casas, Fernando; Murua, Ander (Cambridge University Press, 2024-09-04)

[EN] This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely ...
Splitting methods in the numerical integration of non-autonomous dynamical systems

Blanes Zamora, Sergio; Casas Perez, Fernando; Murua, Ander (Springer-Verlag, 2012)

[EN] We present a procedure leading to efficient splitting schemes for the time integration of explicitly time dependent partitioned linear differential equations arising when certain partial differential equations are ...
Symmetric-conjugate splitting methods for linear unitary problems

Bernier, J.; Blanes Zamora, Sergio; Escorihuela-Tomàs, A.; Casas, F. (Springer-Verlag, 2023-11-10)

[EN] We analyze the preservation properties of a family of reversible splitting methods when they are applied to the numerical time integration of linear differential equations defined in the unitary group. The schemes ...
Symplectic time-average propagators for the Schrodinger equation with a time-dependent Hamiltonian

Blanes Zamora, Sergio; Casas, Fernando; Murua, Ander (American Institute of Physics, 2017-03-21)

[EN] Several symplectic splitting methods of orders four and six are presented for the step-by-step time numerical integration of the Schrodinger equation when the Hamiltonian is a general explicitly time-dependent real ...