In this paper we focus on the analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein–Gordon equations. A novel energy-preserving scheme is developed based on the discrete gradient method and the Duhamel principle. The local error, global convergence and nonlinear stability of the new scheme are analysed in detail. Numerical experiments are implemented to compare with existing numerical methods in the literature, and the numerical results show the remarkable efficiency of the new energy-preserving scheme presented in this paper.

中文翻译：

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求解高维非线性Klein-Gordon方程的能量守恒方案的表述和分析

在本文中，我们专注于求解高维非线性Klein-Gordon方程的能量保存方案的分析。基于离散梯度法和Duhamel原理，提出了一种新型的节能方案。详细分析了新方案的局部误差，全局收敛性和非线性稳定性。通过数值实验与文献中已有的数值方法进行比较，数值结果表明了本文提出的新型节能方案的显着效率。