A dissipation-preserving finite-difference scheme for a generalized Higgs boson equation in the de Sitter space-time

摘要

For the first time in the literature, a dissipation-preserving computational technique to approximate the solutions of a dissipative generalization of the Higgs boson equation in the de Sitter space-time is proposed. The model is a multidimensional system which considers a generalized potential and a general time-dependent diffusion coefficient. The system has an associated energy functional which is dissipated in time. Motivated by this fact, we propose a finite-difference methodology to approximate the solutions of the mathematical model. In addition to the numerical approximation for the solutions of the system, we propose also a discrete energy functional which is dissipated with respect to the discrete time. Using a computer implementation in two spatial dimensions, we provide some simulations that confirm the presence of bubble-like solutions, in agreement with the theory available in the literature. (C) 2020 Elsevier Ltd. All rights reserved.