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Listar por autor "Blanes Zamora, Sergio"

Mostrando ítems 1-20 de 62

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An effcient algorithm based on splitting for the time integration of the Schrödinger equation

Blanes Zamora, Sergio; Casas, Fernando; Murua, Ander (Elsevier, 2015-12-15)

We present a practical algorithm based on symplectic splitting methods intended for the numerical integration in time of the Schrödinger equation when the Hamiltonian operator is either time-independent or changes slowly ...
An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrodinger equation

Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando; Seydaoglu, Muaz (Elsevier, 2022-04)

[EN] We present a practical algorithm to approximate the exponential of skew-Hermitian matrices up to round-off error based on an efficient computation of Chebyshev polynomials of matrices and the corresponding error ...
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 ...
Cálculo de trayectorias de satélites

Expósito Brioso, Diego (Universitat Politècnica de València, 2017-07-27)

El número de satélites que orbitan la tierra ha sufrido un incremento enorme en los últimos años. El control y la precisión de las trayectorias de los mismos son cada vez más exigentes y por tanto resulta necesario poder ...
Comparación de los métodos directos de resolución de SEL con Gauss-Seidel

Romero Bauset, José Vicente; Blanes Zamora, Sergio; Cortés López, Juan Carlos; Roselló Ferragud, María Dolores (Universitat Politècnica de València, 2013-06-26)

Consideramos el sistema de ecuaciones lineales, M x = d, con M la matriz de Hilbert de tamaño n y d la suma de la filas de M. El sistema anterior se resolverá usando los algoritmos de Gauss-Seidel y métodos directos. Se ...
COMPLEMENTOS DE ECUACIONES DIFERENCIALES: RESOLUCIÓN ANALÍTICA, EDPs Y MATHEMATICA

Sánchez Ruiz, Luis Manuel; Blanes Zamora, Sergio (Editorial Universitat Politècnica de València, 2012-11-29)

'Esta publicación muestra cómo resolver ecuaciones diferenciales ordinarias por desarrollos en series de potencias y ecuaciones diferenciales en derivadas parciales, principalmente relacionadas con problemas clásicos como ...
Computing the Matrix Exponential with an Optimized Taylor Polynomial Approximation

Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando (MDPI AG, 2019-12)

[EN] 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 ...
Computing the matrix sine and cosine simultaneously with a reduced number of products

Seydaoglu, Muaz; Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando (Elsevier, 2021-05)

[EN] 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 ...
Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear evolution equations of parabolic type

Blanes Zamora, Sergio; Casas, Fernando; Mechthild Thalhammer (Oxford University Press, 2018)

[EN] 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 ...
Convergence analysis of high-order commutator-free quasi-Magnus exponential integrators for nonautonomous linear Schrodinger equations

Blanes Zamora, Sergio; Casas, Fernando; González, Cesáreo; Thalhammer, Mechthild (Oxford University Press, 2021-01)

[EN] This work is devoted to the derivation of a convergence result for high-order commutator-free quasi-Magnus (CFQM) exponential integrators applied to nonautonomous linear Schrodinger equations; a detailed stability and ...
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 ...
Efficient time integration methods for Gross-Pitaevskii equations with rotation term

Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando; Thalhammer, Mechthild (American Institute of Mathematical Sciences, 2019-12)

[EN] 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, ...
Error analysis of splitting methods for the time dependent Schrodinger equation

Blanes Zamora, Sergio; Casas, Fernando; Murua, Ander (Society for Industrial and Applied Mathematics, 2011)

A typical procedure to integrate numerically the time dependent Schrodinger equation involves two stages. In the first stage one carries out a space discretization of the continuous problem. This results in the linear ...
Evaluación continua, clase inversa y cooperación activa en Matemáticas para ingenieros

Sánchez Ruiz, Luis Manuel; Blanes Zamora, Sergio; Capilla Romá, Maria Teresa; García Mora, María Belén; LLobregat-Gomez, N.; Moll López, Santiago Emmanuel; Moraño Fernández, José Antonio; Roselló, María-Dolores (Facultad de Ciencias. Departamento de Matemáticas Fundamentales. UNED, 2018)

[ES] La Universitat Politècnica de Valencia (UPV) facilita la creación de equipos de innovación y calidad educativa (EICE). Uno de dichos equipos es GRIM4E (GRoup of Innnovative Methodologies and Assessment For Engineering ...
Explicit adaptive symplectic integrators for solving Hamiltonian systems

Blanes Zamora, Sergio; Iserles, Arieh (Springer Verlag (Germany), 2012-11)

We consider Sundman and Poincaré transformations for the long-time numerical integration of Hamiltonian systems whose evolution occurs at different time scales. The transformed systems are numerically integrated using ...
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) ...
Exponential integrators for coupled self-adjoint non-autonomous partial differential systems

Ponsoda Miralles, Enrique; Blanes Zamora, Sergio (Elsevier, 2014-09)

We consider the numerical integration of coupled self-adjoint non-autonomous partial differential systems. Under convergence conditions, the solution can be written as a series expansion where each of its terms correspond ...
Exponential propagators for the Schrödinger equation with a time-dependent potential

Bader, Philipp; Kopylov, Nikita; Blanes Zamora, Sergio (American Institute of Physics, 2018)

[EN] We consider the numerical integration of the Schrodinger equation with a time-dependent Hamiltonian given as the sum of the kinetic energy and a time-dependent potential. Commutator-free (CF) propagators are exponential ...
Fourier methods for the perturbed harmonic oscillator in linear and nonlinear Schrödinger equations

Bader, Philipp; Blanes Zamora, Sergio (American Physical Society, 2011)

[EN] We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with ...
Fourier-Hermite methods for perturbed harmonic oscillator problems

Bader, Philipp Karl Heinz (Universitat Politècnica de València, 2011-07-26)

In this work, we address the problem of solving non-linear Schrödinger equations numerically and find that an exact particular splitting technique shows superior performance to commonly used methods. We consider the ...