TY - JOUR
T1 - Stability Analysis of Runge-Kutta Methods for Nonlinear Neutral Volterra Delay-Integro-Differential Equations
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 537
EP - 561
PY - 2011
DA - 2011/04
SN - 4
DO - http://doi.org/10.4208/nmtma.2011.m1041
UR - https://global-sci.org/intro/article_detail/nmtma/5982.html
KW - Neutral differential equations, Volterra delay-integro-differential equations, RungeKutta methods, stability.
AB - <p style="text-align: justify;">This paper is concerned with the numerical stability of implicit Runge-Kutta
methods for nonlinear neutral Volterra delay-integro-differential
equations with constant delay. Using a Halanay inequality
generalized by Liz and Trofimchuk, we give two sufficient conditions
for the stability of the true solution to this class of equations.
Runge-Kutta methods with compound quadrature rule are considered.
Nonlinear stability conditions for the proposed methods are
derived. As an illustration of the application of these
investigations, the asymptotic stability of the presented methods
for Volterra delay-integro-differential equations is proved under
some weaker conditions than those in the literature. An extension of the stability results to such equations with weakly singular kernel is also discussed.</p>