The asymptotic stability of theoretical and numerical solutions for systems of neutral multidelay-differential equations
type: Item
instance of: scholarly article
title: The asymptotic stability of theoretical and numerical solutions for systems of neutral multidelay-differential equations
zbMATH Open document ID: 0924.65079
DOI: 10.1007/BF02871977
published in: Science in China. Series A
publication date: 1999-11-16T00:00:00Z
review text: Consider the following problem for a system of linear delayed differential equations: \[ {d\over dt}\Biggl[x(t)- \sum^k_{m=1} N_mx(t- \tau_m)\Biggr]= Lx(t)+ \sum^k_{m= 1}M_mx(t- \tau_m),\quad t>0, \] \[ x(t)= \varphi(t),\quad -\tau\leq t\leq 0, \] where \(N_m\), \(L\) and \(M_m\) \((1\leq m\leq k)\) are constant complex \(p\times p\)-matrices, \(\tau_m>0\) \((1\leq m\leq k)\) are constant delays and \(\tau= \max\tau_m\). The authors give a sufficient condition for the asymptotic stability of the exact solution and establish a connection between this stability and the \(A\)-stability of a multistep Runge-Kutta method.
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34K40
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 65L07
zbMATH DE Number: 1281381
zbMATH Keywords: systems of neutral multidelay-differential equations
zbMATH Keywords: asymptotic stability
zbMATH Keywords: \(A\)-stability
zbMATH Keywords: multistep Runge-Kutta method
author: Cheng-Jian Zhang
author: Shuzi Zhou
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1281381