The present work introduces a numerical scheme that preserves the dissipation of energy of the Higgs boson equation in the de Sitter space-time. More precisely, the model considered in this work is a mathematical generalization of Higgs' model which includes a general time-dependent diffusion coefficient and a generalized potential. The mathematical system is dissipative, and we propose an implicit discrete method which approximates consistently the radially symmetric solutions of the continuous system. At the same time, a discrete energy functional is presented, and we prove that, as its continuous counterpart, the numerical technique dissipates the energy of the discrete system. The properties of consistency, stability and convergence of the numerical model are proved rigorously. To confirm the theoretical results, we approximate some radially symmetric solutions of the classical Higgs boson equation in the de Sitter space-time. In particular, the numerical results confirm the stability and the formation of bubble-like solutions.

本工作介绍了一种数值方案，该方案在de Sitter时空中保留了希格斯玻色子方程的能量耗散。更准确地说，在这项工作中考虑的模型是希格斯模型的数学概括，其中包括广义的时间相关扩散系数和广义势。数学系统是耗散的，因此我们提出了一种隐式离散方法，该方法始终如一地近似连续系统的径向对称解。同时，提出了一个离散的能量函数，并且我们证明，作为其连续的对等物，数值技术消散了离散系统的能量。严格证明了数值模型的一致性，稳定性和收敛性。为了确认理论结果，我们在de Sitter时空中近似经典Higgs玻色子方程的一些径向对称解。特别地，数值结果证实了稳定性和气泡状溶液的形成。