Stability Analysis Of A Class Of Nonlinear Hysteretic Differential Algebraic Equations And BDF 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 simulation.For the moment, stability and numerical methods for linear DDAEs have been very intensively studied, we are aware of very little work on nonlinear DDAEs. In this paper, we investigate the stability and asymptotic stability of the nonlinear DDAEs and numerical methods. First,according the definition of stability and asymptotic stability, we give and prove a sufficient condition. Then, we discuss the stability and asymptotic stability of 2 step Backward Differential Formula(BDF),which applied to the stable and asymptotic stable nonlinear DDAEs. Lastly, some numerical experiments are carried out to demonstrate the conclusion is right.