[EN] 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 Schrodinger and ...
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 ...
[EN] Standard numerical schemes with time-step h deteriorate (e.g. like epsilon(-2)h(2)) in the presence of a small semiclassical parameters in the time-dependent Schrodinger equation. The recently introduced semiclassical ...
[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 ...
Using a Newtonian model of the Solar System with all 8 planets, we perform extensive tests on various symplectic integrators of high orders, searching for the best splitting scheme for long term studies in the Solar System. ...
[EN] The class of commutator-free quasi-Magnus (CFQM) exponential integrators provides a favourable alternative to standard Magnus integrators, in particular for large-scale applications arising in the time integration of ...
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 ...
Roselló Ferragud, María Dolores; Blanes Zamora, Sergio; Cortés López, Juan Carlos; Romero Bauset, José Vicente(Universitat Politècnica de València, 2013-07-03)
Consideramos el sistema de ecuaciones lineales, M x = d, con M=[dd, -1, 0;-1, dd, -1;0, -1, dd]; d = [2,8,-6]'; donde los elementos de la diagonal principal de M, dd, es un dato a introducir, siendo dd>=2 para que no haya ...
Roselló Ferragud, María Dolores; Ginestar Peiro, Damián; Blanes Zamora, Sergio(Editorial Universitat Politècnica de València, 2020-07-13)
En el libro se presenta una introducción a los diferentes temas relacionados con la resolución numérica de ecuaciones diferenciales ordinarias y en derivadas parciales.
Se comienza introduciendo distintos modelos matemáticos ...
We consider Magnus integrators to solve linear-quadratic N-player differential games.
These problems require to solve, backward in time, non-autonomous matrix Riccati
differential equations which are coupled with the ...
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 ...
The analysis of heat conduction through a solid with heat generation leads to a linear matrix differential equation with separated boundary conditions. We present a symmetric second order exponential integrator for the ...
[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 ...
[EN] We present a novel class of integrators for differential equations that are suitable for parallel in time computation, whose structure can be considered as a generalization of the extrapolation methods. Starting with ...
[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 ...
Blanes Zamora, Sergio; Casas, Fernando; Sanz-Serna, J. M.(Society for Industrial and Applied Mathematics, 2014)
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the ...
[EN] We analyze composition methods with complex coefficients exhibiting the so-called ¿symmetry-conjugate¿ pattern in their distribution. In particular, we study their behavior with respect to preservation of qualitative ...
[EN] We show how to build explicit symmetric second order methods for solving ordinary differential equations. These methods are very useful when low accuracy is required or when higher order ones by extrapolation or ...
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 ...
[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 ...