Abstract
We perform some simulations of the semilinear Klein–Gordon equation in the de Sitter spacetime. We reported the accurate numerical results of the equation with the structure-preserving scheme (SPS) in an earlier publication (Tsuchiya and Nakamura, J Comput Appl Math 361:396–412, 2019). To investigate the factors for the stability and accuracy of the numerical results with SPS, we perform some simulations with three discretized formulations. The first formulation is the discretized equations with SPS, the second one is with SPS that replaces the second-order difference as the standard second-order central difference, and the third one is with SPS that replaces the discretized nonlinear term as the standard discretized expression. As a result, the above two replacements in SPS are found to be effective for accurate simulations. On the other hand, the ingenuity of replacing the second-order difference in the first formulation is not effective for maintaining the stability of the simulations.
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Acknowledgements
The authors thank the anonymous referees for their many helpful comments that improved the paper. T.T. and M.N. were partially supported by JSPS KAKENHI Grant Number 21K03354. T.T. was partially supported by JSPS KAKENHI Grant Number 20K03740 and Grant for Basic Science Research Projects from The Sumitomo Foundation. M.N. was partially supported by JSPS KAKENHI Grant Number 16H03940.
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Tsuchiya, T., Nakamura, M. (2023). Numerical Simulations of Semilinear Klein–Gordon Equation in the de Sitter Spacetime with Structure-Preserving Scheme. In: Kähler, U., Reissig, M., Sabadini, I., Vindas, J. (eds) Analysis, Applications, and Computations. ISAAC 2021. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-36375-7_42
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DOI: https://doi.org/10.1007/978-3-031-36375-7_42
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