arXiv subjects

Alejandro Escorihuela-Tomàs

Publications and source records attributed to Alejandro Escorihuela-Tomàs.

8 recordsLinked to original sources

arXiv2026

D-splitting methods: 2N -storage embedded explicit pseudo-geometric Runge-Kutta methods using splitting methods

Low-storage explicit Runge-Kutta schemes are particularly popular for the numerical integration of time-dependent partial differential equations based on the method-of-lines due to their efficiency and their reduced memory requirements. We show that D-splitting methods, splitting methods on the extended phase space, can be used as high performance 2N-storage embedded explicit RK methods without a third storage register. They are pseudo-geometric methods preserving some of the qualitative properties of the exact solution up to a higher order than the order of the method. Some of their properties are analysed, to build new tailored methods, and are tested on numerical examples.

math.NA↗

arXiv2026

Efficient symplectic integrators for cubic and quartic potentials

We present a set of new, efficient high-order symplectic methods designed for Hamiltonian systems with cubic or quartic potentials. By demonstrating that polynomial potentials require fewer order conditions, we develop schemes that outperform both standard symmetric compositions of second-order methods and existing RKN splitting methods. Numerical results confirm their improved efficiency over state-of-the-art alternatives found in the literature.

math.NA↗

arXiv2024

Families of efficient low order processed composition methods

New families of composition methods with processing of order 4 and 6 are presented and analyzed. They are specifically designed to be used for the numerical integration of differential equations whose vector field is separated into three or more parts which are explicitly solvable. The new schemes are shown to be more efficient than previous state-of-the-art splitting methods.

math.NA↗

arXiv2023

Symmetric-conjugate splitting methods for linear unitary problems

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 involve complex coefficients and are conjugated to unitary transformations for sufficiently small values of the time step-size. New and efficient methods up to order six are constructed and tested on the linear Schrödinger equation.

math.NA↗

arXiv2021

High order integrators obtained by linear combinations of symmetric-conjugate compositions

A new family of methods involving complex coefficients for the numerical integration of differential equations is presented and analyzed. They are constructed as linear combinations of symmetric-conjugate compositions obtained from a basic time-symmetric integrator of order 2n (n $\ge$ 1). The new integrators are of order 2(n + k), k = 1, 2, ..., and preserve time-symmetry up to order 4n + 3 when applied to differential equations with real vector fields. If in addition the system is Hamiltonian and the basic scheme is symplectic, then they also preserve symplecticity up to order 4n + 3. We show that these integrators are well suited for a parallel implementation, thus improving their efficiency. Methods up to order 10 based on a 4th-order integrator are built and tested in comparison with other standard procedures to increase the order of a basic scheme.

math.NA↗

arXiv2021

On symmetric-conjugate composition methods in the numerical integration of differential equations

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 properties when projected on the real axis and we compare them with the usual left-right palindromic compositions. New schemes within this family up to order 8 are proposed and their efficiency is tested on several examples. Our analysis shows that higher-order schemes are more efficient even when time step sizes are relatively large.

math.NA↗

arXiv2020

Composition Methods for Dynamical Systems Separable into Three Parts

New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a way that each part is explicitly solvable. The methods are obtained by applying different optimization criteria and preserve geometric properties of the continuous problem by construction. Different numerical examples exhibit their improved performance with respect to previous splitting methods in the literature.

math.NA↗

arXiv2017

Quasistationary solutions of scalar fields around collapsing self-interacting boson stars

There is increasing numerical evidence that scalar fields can form long-lived quasi-bound states around black holes. Recent perturbative and numerical relativity calculations have provided further confirmation in a variety of physical systems, including both static and accreting black holes, and collapsing fermionic stars. In this work we investigate this issue yet again in the context of gravitationally unstable boson stars leading to black hole formation. We build a large sample of spherically symmetric initial models, both stable and unstable, incorporating a self-interaction potential with a quartic term. The three different outcomes of unstable models, namely migration to the stable branch, total dispersion, and collapse to a black hole, are also present for self-interacting boson stars. Our simulations show that for black-hole-forming models, a scalar-field remnant is found outside the black-hole horizon, oscillating at a different frequency than that of the original boson star. This result is in good agreement with recent spherically symmetric simulations of unstable Proca stars collapsing to black holes.

gr-qc↗