Asymptotic Stabiltity Of Neutral Delay Differential-Algebraic Equations With Multiple Delays And Numerical Methods

Delay differential-algebraic equations (DDAEs), which has both delay and algebraic constraints, provides effective mathematical model for scientific and engineering applications problems, such as computer-aided design, chemical process simulation, circuit analysis, optimal control, real-time simulationand management system. Neutral delay differential-algebraic equations with multiple delay terms (NMDDAEs) is a kind of DDAEs with more complicated structure since the unknow function not only has multiple delay terms but also the derivatives of unknow function has multiple delay terms. However, because of the complexity of DDAEs, it becomes quite difficult to obtain the analytic solutions.Therefore, it is necessary to investigate the numerical methods for DDAEs and they have become one of the most chief and principal methods to solve DDAEs. Moreover, effective and reliable computational methods and the stability of numerical methods are the key problems we have to face in the research of the numerical solution.This thesis is concerned with the asymptotic stability oanalytical and numerical solutions of neutral delay differential-algebraic equations with multiple delays (NMDDAEs). Onthe basis of a sufficient condition under which linear NMDDAEs with constant coefficients is asymptotically stable, we dwellon the asymptotic stability of two numerical methods. First, we discuss the asymptotic stability of continuous Runge-Kutta methods when it is applied to asymptotically stable NMDDAEs. Then, we discuss the asymptotic stability of two step Runge-Kutta methods when it is applied to asymptotically stable NMDDAEs. Finally, some numerical experiments are carried out to demonstrate our conclusions. Moreover, we can easily obtain that TSRK methods is better thancontinuous RK methods.