TY - JOUR
T1 - Nonlinear Stability of Natural Runge-Kutta Methods for Neutral Delay Differential Equations
AU - Zhang , Cheng-Jian
JO - Journal of Computational Mathematics
VL - 6
SP - 583
EP - 590
PY - 2002
DA - 2002/12
SN - 20
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/8943.html
KW - Nonlinear stability, Neutral delay differential equations, Natural Runge-Kutta methods.
AB - <p style="text-align: justify;">This paper first presents the stability analysis of theoretical solutions for a class of nonlinear neutral delay-differential equations (NDDEs). Then the numerical analogous results, of the natural Runge-Kutta (NRK) methods for the same class of nonliner NDDEs, are given. In particular, it is shown thar the ($k,l$)-algebraic stability of a RK method for ODEs implies the generalized asymptotic stability and the global stability of the induced NRK method.</p>