@Article{CMR-40-413,
author = {Wang , Jialing and He , Yali},
title = {A High-Order Meshless Energy-Preserving Algorithm for the Beam Equation},
journal = {Communications in Mathematical Research },
year = {2024},
volume = {40},
number = {4},
pages = {413--436},
abstract = {<p style="text-align: justify;">In this paper, a meshless energy-preserving algorithm which can be
arbitrarily high-order in temporal direction for the beam equation has been
proposed. Based on the method of lines, we first use the radial basis function quasi-interpolation method to discretize spatial variable and obtain a semi-discrete Hamiltonian system by using the premultiplication of a diagonal matrix. Then, symplectic Runge-Kutta method that can conserve quadratic invariants exactly has been used to discretize the temporal variable, which yields
a fully discrete meshless scheme. Due to the specific quadratic energy expression of the beam equation, the proposed meshless scheme here is not only
energy-preserving but also arbitrarily high-order in temporal direction. Besides uniform and nonuniform grids, numerical experiments on random grids
are also conducted, which demonstrate the properties of the proposed scheme
very well.</p>},
issn = {2707-8523},
doi = {https://doi.org/10.4208/cmr.2024-0018},
url = {http://global-sci.org/intro/article_detail/cmr/23700.html}
}