STABILITIES OF (A,B,C) AND NPDIRK METHODS FOR SYSTEMS OF NEUTRAL DELAY-DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS

摘要

Consider the following neutral delay-differential equations with multiple delays (NMDDE) y′(t) = Ly(t) + Σ from j=1 to m [M_(jy) (t - T_j) + N_(jy′)(t -T_j)], t ≥0, (0.1) where T > 0, L, M_j and N_j are constant complex-value d x 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 are 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 methods. We also investigate the stability of a special class of NPDIRK methods by analyzing their stability behaviors of the solutions of (0.1).