Numerical simulations of semi-linear Klein-Gordon equations in the de Sitter spacetime with structure preserving scheme
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We perform some simulations of the Klein-Gordon equation in the de Sitter spacetime. We reported the stable and high-precision numerical results of the equation using the structure preserving scheme (SPS) in an earlier publication (Tsuchiya and Nakamura in J. Comput. Appl. Math. 361: 396–412, 2019). To investigate the factors of the stability and accuracy of the simulations with SPS, we perform some simulations with three discretized formulations. The first formulation is the discretized equations with SPS, the second is with SPS which replaced the second derivative term as the standard difference, and the third is with SPS which replaced the non-linear term as the standard expression. As a result, the above two replacements in SPS are found to be effective for stable and high-precision simulations.
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