TY - JOUR
T1 - Numerical Stability and Oscillations of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments of Advanced Type
AU - Wang , Qi
JO - Communications in Mathematical Research 
VL - 2
SP - 131
EP - 142
PY - 2021
DA - 2021/05
SN - 29
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19018.html
KW - numerical solution, Runge-Kutta method, asymptotic stability, oscillation.
AB - <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>