@Article{CMR-29-2,
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 = {2013},
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/2013-CMR-19018},
url = {https://global-sci.com/article/81787/numerical-stability-and-oscillations-of-runge-kutta-methods-for-differential-equations-with-piecewise-constant-arguments-of-advanced-type}
}