@Article{CMR-29-131,
author = {Wang , Qi},
title = {Numerical Stability and Oscillations of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments of Advanced Type},
journal = {Communications in Mathematical Research },
year = {2021},
volume = {29},
number = {2},
pages = {131--142},
abstract = {<p style="text-align: justify;">For differential equations with piecewise constant arguments of advanced
type, numerical stability and oscillations of Runge-Kutta methods are investigated.
The necessary and sufficient conditions under which the numerical stability region
contains the analytic stability region are given. The conditions of oscillations for the
Runge-Kutta methods are obtained also. We prove that the Runge-Kutta methods
preserve the oscillations of the analytic solution. Moreover, the relationship between
stability and oscillations is discussed. Several numerical examples which confirm the
results of our analysis are presented.</p>},
issn = {2707-8523},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cmr/19018.html}
}