@article{Gao2025, 
author = {Dongjie Gao and Peiguo Zhang and Longqin Wang and Zhenlong Dai and Yonglei Fang},
title = {A novel high-order symmetric and energy-preserving continuous-stage Runge-Kutta-Nyström Fourier pseudo-spectral scheme for solving the two-dimensional nonlinear wave equation},
year = {2025},
journal = {AIMS Mathematics},
volume = {10},
number = {3},
pages = {6764-6787},
keywords = {two dimensional nonlinear wave equations, energy-preserving method, symmetry, continuous-stage Runge-Kutta-Nyström method, Fourier pseudo-spectral method},
url = {https://www.sciopen.com/article/10.3934/math.2025310},
doi = {10.3934/math.2025310},
abstract = {The primary objective of this research is to develop a novel high-order symmetric and energy-preserving method for solving two-dimensional nonlinear wave equations. Initially, the nonlinear wave equation is reformulated as an abstract Hamiltonian ordinary differential equation (ODE) system with separable energy in an appropriate infinite-dimensional function space. Subsequently, an energy-preserving and symmetric continuous-stage Runge-Kutta-Nyström time-stepping scheme is derived. After approximating the spatial differential operator using the two-dimensional Fourier pseudo-spectral method, we derive an energy-preserving fully discrete scheme. A rigorous error analysis demonstrates that the proposed method can achieve at least fourth-order accuracy in time. Finally, numerical examples are provided to validate the accuracy, efficiency, and long-term energy conservation of the method.}
}