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arXiv · 1905.08939

On the numerical experiments of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime

Takuya Tsuchiya·Makoto Nakamura
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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.

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Takuya Tsuchiya, Makoto Nakamura. 2019-05-22. On the numerical experiments of the Cauchy problem for semi-linear Klein-Gordon equations in the de Sitter spacetime. https://doi.org/10.1016/j.cam.2019.05.005

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