[EN] Many important applications are modelled by differential equations with positive solutions. However, it remains an outstanding open problem to develop numerical methods that are both (i) of a high order of accuracy ...
[EN] We consider the numerical propagation of models that combine both quantum and classical degrees of freedom, usually, electrons and nuclei, respectively. We focus, in our computational examples, on the case in which ...
[EN] 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 ...
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 ...
[EN] Efficient splitting algorithms for the Schrödinger eigenvalue problem
with perturbed harmonic oscillator potentials in higher dimensions are considered.
The separability of the Hamiltonian makes the problem suitable ...
Bader, Philipp; Blanes Zamora, Sergio; Casas, Fernando(American Institute of Physics (AIP), 2013-09-28)
The Schrodinger eigenvalue problem is solved with the imaginary time propagation technique. The separability of the Hamiltonian makes the problem suitable for the application of splitting methods. High order fractional ...
[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 ...
Seydaoglu, Muaz(Universitat Politècnica de València, 2016-10-07)
[EN] This thesis addresses the treatment of perturbed problems with splitting methods. After motivating these problems in Chapter 1, we give a thorough introduction in Chapter 2, which includes the objectives, several basic ...
[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 ...
[EN] We present structure preserving integrators for solving linear quadratic optimal control
problems. The goal is to build methods which can also be used for the integration of
nonlinear problems if they are previously ...
Blanes Zamora, Sergio; Calvo, M.P.; Casas, F.; Sanz-Serna, J. M.(Society for Industrial and Applied Mathematics, 2021)
[EN] We construct integrators to be used in Hamiltonian (or Hybrid) Monte Carlo sampling. The new integrators are easily implementable and, for a given computational budget, may deliver five times as many accepted proposals ...
[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 ...
[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 ...
[EN] 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 ...
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 ...
Bader, Philipp; Blanes Zamora, Sergio; Seydaoglu, Muaz(Society for Industrial and Applied Mathematics, 2015)
[EN] We propose splitting methods for the computation of the exponential of perturbed matrices which can be written as the sum A = D+epsilon B of a sparse and efficiently exponentiable matrix D with sparse exponential e(D) ...
Blanes Zamora, Sergio(Society for Industrial and Applied Mathematics, 2018)
[EN] In this work we show how to numerically integrate nonautonomous differential equations by solving alternate time-averaged differential equations. Given a quadrature rule of order 2s or higher for s = 1, 2, . . . , we ...
We consider time-averaging methods based on the Magnus series expansion jointly with exponential integrators for the numerical integration of general linear non-homogeneous differential equations. The schemes can be ...