Stability Of Neutral Delay Differential Algebraic More Systematic Analysis

Neutral delay differential-algebraic systems is widely used in biology,financeand physics and so on.The stability study can provide theoretical support forengineering and technology field. Due to the constraint of delay and algebraicconditions, it is very difficult for us to obtain the analytic solutions of stability ofneutral delay differential-algebraic systems（NDAES）.Therefore, it is necessary toinvestigate the numerical methods for NDAES.This paper adopts three kinds of methods to analyze the numerical stability ofneutral multidelay differential algebraic system(NMDAES). First of all,it discussed thenumerical stability of block θ-method solve the NMDAES, and it proved thatA-stable θ-method can preserve the asymptotic stability of underlying systems,aftergiving some conditions. Based on this, it discussed the numerical stability of linearmultistep method to solve the NMDAES, and it proved that A-stable linear multistepmethods can preserve the asymptotic stability of underlying systems,after givingsome conditions. At last,we study the numerical stability of Runge-Kutta-methodsolving NMDAES.It has shown A-stable Runge-Kutta-method can keep the asymptoticstability of underlying systems,after giving some conditions...