@Article{CiCP-7-5,
author = {},
title = {A Weighted Runge-Kutta Method with Weak Numerical Dispersion for Solving Wave Equations},
journal = {Communications in Computational Physics},
year = {2010},
volume = {7},
number = {5},
pages = {1027--1048},
abstract = {<p style="text-align: justify;">In this paper, we propose a weighted Runge-Kutta (WRK) method to solve
the 2D acoustic and elastic wave equations. This method successfully suppresses the
numerical dispersion resulted from discretizing the wave equations. In this method,
the partial differential wave equation is first transformed into a system of ordinary
differential equations (ODEs), then a third-order Runge-Kutta method is proposed
to solve the ODEs. Like the conventional third-order RK scheme, this new method
includes three stages. By introducing a weight to estimate the displacement and its
gradients in every stage, we obtain a weighted RK (WRK) method. In this paper, we
investigate the theoretical properties of the WRK method, including the stability criteria,
numerical error, and the numerical dispersion in solving the 1D and 2D scalar
wave equations. We also compare it against other methods such as the high-order
compact or so-called Lax-Wendroff correction (LWC) and the staggered-grid schemes.
To validate the efficiency and accuracy of the method, we simulate wave fields in the
2D homogeneous transversely isotropic and heterogeneous isotropic media. We conclude
that the WRK method can effectively suppress numerical dispersions and source
noises caused in using coarse grids and can further improve the original RK method
in terms of the numerical dispersion and stability condition.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2009.09.088},
url = {https://global-sci.com/article/81014/a-weighted-runge-kutta-method-with-weak-numerical-dispersion-for-solving-wave-equations}
}