(untitled) (Journal of Computational Mathematics, 2003)
Consider the following neutral delay-differential equations with multiple delays (NMDDE)y'(t)=Ly(t)+_j=1^m[M_jy(t-τ_j)+N_jy'(t-τ_j)], t≥ 0, (0.1) where τ>0, L, M_j and N_j are constant complex- value d×d matrices. A sufficient condition for the asymptotic stability of NMDDE system (0.1) is given. The stability of Butcher's (A,B,C)-method for systems of NMDDE is studied. In addition, we present a parallel diagonally-implicit iteration RK (PDIRK) methods (NPDIRK) for systems of NMDDE, which is easier to be implemented than fully implicit RK methos. We also investigate the stability of a special class of NPDIRK methods by analyzing their stability behaviors of the solutions of (0.1).