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

• 来源期刊: 计算数学（英文版）
• 学科: 数学
• 关键词: Neutral delay differential equations (A B C)-method RK method Paralleldiagonally-implicit iteration RK method.
• 年，卷（期）: 2003,（3）
• 页码范围: 375-382
• 页数: 8页
• 分类号: O1
• 语种: 英文

摘要

Consider the following neutral delay-differential equations with multiple delays (NMDDE)my'(t) ＝ Ly(t) + ∑[Mjy(t - τj) + Njy'(t - τj)], t ≥ 0, (0.1)j＝1where τ＞ 0, L, Mj and Nj are constant complex-value d×d matrices. A sufficient conditionfor 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 paralleldiagonally-implicit iteration RK (PDIRK) methods(NPDIRK) for systems of NMDDE,which is easier to be implemented than fully implicit RK methods. We also investigatethe stability of a special class of NPDIRK methods by analyzing their stability behaviorsof the solutions of (0.1).