@Article{IJNAM-16-2,
author = {Liu, Changying and Wei, Shi and Xinyuan, Wu},
title = {Numerical Analysis of an Energy-Conservation Scheme for Two-Dimensional Hamiltonian Wave Equations with Neumann Boundary Conditions},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2019},
volume = {16},
number = {2},
pages = {319--339},
abstract = {<p style="text-align: justify;">In this paper, an energy-conservation scheme is derived and analysed for solving
Hamiltonian wave equations subject to Neumann boundary conditions in two dimensions. The
energy-conservation scheme is based on the blend of spatial discretisation by a fourth-order finite
difference method and time integration by the Average Vector Field (AVF) approach. The spatial
discretisation via the fourth-order finite difference leads to a particular Hamiltonian system of
second-order ordinary differential equations. The conservative law of the discrete energy is established,
and the stability and convergence of the semi-discrete scheme are analysed. For the time
discretisation, the corresponding AVF formula is derived and applied to the particular Hamiltonian
ODEs to yield an efficient energy-conservation scheme. The numerical simulation is implemented
for various cases including a linear wave equation and two nonlinear sine-Gordon equations.
The numerical results demonstrate the spatial accuracy and the remarkable energy-conservation
behaviour of the proposed energy-conservation scheme in this paper.</p>},
issn = {2617-8710},
doi = {https://doi.org/2019-IJNAM-12806},
url = {https://global-sci.com/article/83064/numerical-analysis-of-an-energy-conservation-scheme-for-two-dimensional-hamiltonian-wave-equations-with-neumann-boundary-conditions}
}