On the numerical experiments of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime
arXiv:1905.08939 · doi:10.1016/j.cam.2019.05.005
Abstract
The computational analysis of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime is considered. Several simulations are performed to show the time-global behaviors of the solutions of the equations in the spacetime based on the structure-preserving scheme. It is remarked that the sufficiently large Hubble constant yields the strong diffusion-effect which gives the long and stable simulations for the defocusing semi-linear terms. The reliability of the simulations is confirmed by the preservation of the numerically modified Hamiltonian of the equations.
25 pages, 18 figures