The asymptotic stability of theoretical and numerical solutions for systems of neutral multidelay-differential equations
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.
systems of neutral multidelay-differential equations
scientific article; zbMATH DE number 1281381