On the numerical experiments of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime
For researchers studying nonlinear wave equations in curved spacetimes, this provides numerical evidence of stability under large Hubble constants, but the results are incremental and domain-specific.
The paper presents numerical simulations of semi-linear Klein-Gordon equations in de Sitter spacetime, showing that a sufficiently large Hubble constant yields strong diffusion effects enabling long and stable simulations for defocusing nonlinear terms. Reliability is confirmed by preservation of a numerically modified Hamiltonian.
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.