A Fortran-95 algorithm to solve the three-dimensional Higgs boson equation in the de Sitter space-time - Open Research Data - Bridge of Knowledge

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A Fortran-95 algorithm to solve the three-dimensional Higgs boson equation in the de Sitter space-time

Description

A numerically efficient finite-difference technique for the solution of a fractional extension of the Higgs boson equation in the de Sitter space-time is designed. The model under investigation is a multidimensional equation with Riesz fractional derivatives of orders in (0,1)U(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 Hamiltoninan 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. The present algorithm is the first to implement a Hamiltonian discretization of the Higgs boson equation (both fractional and non-fractional) in the de Sitter space-time. More precisely, the present effort 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. Previous efforts used techniques based on the Runge--Kutta method or discretizations that did not preserve the dissipation nor were rigorously analyzed.

Dataset file

higgs.f95
4.6 kB, S3 ETag a17ae1824803454b0c29b01e81d127a4-1, downloads: 54
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File details

License:
Creative Commons: by 4.0 open in new tab
CC BY
Attribution
Software:
Fortran-95

Details

Year of publication:
2020
Verification date:
2020-12-17
Dataset language:
English
Fields of science:
  • mathematics (Natural sciences)
DOI:
DOI ID 10.34808/5fvy-a637 open in new tab
Verified by:
Gdańsk University of Technology

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