de Sitter时空中半线性Klein-Gordon方程的保结构方案数值模拟
Numerical simulations of semilinear Klein--Gordon equation in the de Sitter spacetime with structure-preserving scheme
摘要：
我们在de Sitter时空中对半线性Klein-Gordon方程进行了一些模拟。我们在早期出版物（Tsuchiya和Nakamura在J. COMPUT.应用数学\textbf{361}：396- 412，2019）。为了研究SPS数值结果的稳定性和准确性的因素，我们用三种离散公式进行了一些模拟。第一个公式是用SPS离散方程，第二个公式是用SPS代替二阶差分作为标准二阶中心差分，第三个公式是用SPS代替离散非线性项作为标准离散表达式。结果表明，SPS中的上述两种替换方法对于精确模拟是有效的。另一方面，在第一配方中替换二阶差分的巧妙性对于保持模拟的稳定性是无效的。
英文摘要：
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 in J. Comput. Appl. Math. \textbf{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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