Numerical Stability Of Linear Multistep Methods For Integro Differential-algebraic Equations With Many Delays

Delay differential-algebraic equations(DDAEs) arise in a wide variety of fields,delay integro-differential algebraic equations(DIDAEs) is an important branch ofDDAEs. This thesis is concerned with the numerical stability of DIDAEs withmultiple delays.This thesis is organized as follows:Firstly, we simply introduced the birth of DDEs and its many applications. Wegive an research status of DDEs and the research background of DIDAEs.Secondly, we study DIDAEs with many delays and give a new result about thedistribution of the roots of its characteristic polynomial. Then we derive somesufficient conditions for its stability.Thirdly, solutions of the system are obtained by linear multistep methodscombined with Lagrange interpolation, with the compound quadrature formula, arenumerically stable under suitable conditions. Moreover, numerical examples aregiven which contains strongly A-stable and nonstrongly A-stable two forms forchecking the stability of the linear multistep methods.At last, we concludes this paper and shows the direction of the system.