Energy-preserving and symmetric fourth-order modified AVF Fourier pseudo-spectral methods for nonlinear Hamiltonian wave equations

Changying Liu, Kai Liu and Dongjie Gao

Mathematics and Computers in Simulation (MATCOM), 2026, vol. 249, issue C, 39-55

Abstract: The main objective of this work is to construct a high-order energy-preserving and symmetric fully discrete scheme, which is built upon the application of the fourth-order modified average vector field (MAVF) time integrator and the Fourier pseudo-spectral spatial approximation, for solving the nonlinear Hamiltonian wave equation. Initially, we reformulate the nonlinear Hamiltonian wave equation as an abstract infinite-dimensional separable Hamiltonian ODE system. The energy-preserving and symmetric time-stepping scheme is derived by using the fourth-order modified average vector field integrator. Subsequently, by applying the Fourier pseudo-spectral method to discretize the spatial derivatives of the second-order nonlinear Hamiltonian wave equation, we propose a fully discrete scheme that preserves energy and exhibits temporal reversibility. The rigorous error analysis demonstrates that the temporal accuracy of the proposed scheme achieves O(Δt4) under the low regularity assumption u∈C3([t0,T],Hpm0(Ω)). Finally, the numerical examples are presented to verify the accuracy, efficiency and energy conservation in long-time computation.

Keywords: Hamiltonian wave equation; Energy-preserving method; Symmetry; Modified average vector field; Fourier pseudo-spectral method (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:249:y:2026:i:c:p:39-55

DOI: 10.1016/j.matcom.2026.05.004

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