Abstract
In this work, we design a numerically efficient finite-difference technique for the solution of a fractional extension of the Higgs boson equation in the de Sitter space- time. The model under investigation is a multidimensional equation with Riesz fractional derivatives of orders in (0, 1) boolean OR (1, 2], which considers a generalized potential and a time-dependent diffusion factor. An energy integral for the mathematical model is readily available, and we propose an explicit and consistent numerical technique based on fractional-order centered differences with similar Hamiltonian properties as the continuous model. A fractional energy approach is used then to prove the properties of stability and convergence of the technique. For simulation purposes, we consider both the classical and the fractional Higgs real-valued scalar fields in the (3 + 1)-dimensional de Sitter space-time, and find results qualitatively similar to those available in the literature. The present work is the first paper to report on a Hamiltonian discretization of the Higgs boson equation (both fractional and non-fractional) in the de Sitter space-time and its numerical analysis. More precisely, the present manuscript is the first paper of the literature in which a dissipation-preserving scheme to solve the multi-dimensional (fractional) Higgs boson equation in the de Sitter space-time is proposed and thoroughly analyzed. Indeed, it is worth pointing out that previous efforts used techniques based on the Runge-Kutta method or discretizations that did not preserve the dissipation nor were rigorously analyzed. (c) 2020 Elsevier B.V. All rights reserved.
NSTL
Elsevier