Dynamics Of Linear Multistep Methods For Delay Differential Equations

Delay differential dynamical systems have appeared in areas of applications as diverseas neural networks, optics, biology, automatic control theory. There are many significantachievements on basic theory, stability theory, period solution theory and bifurcation theoryof delay differential systems.Numerical simulation is one of the most important methods to understand dynamicalproperties of delay differential equations. A numerical method which is convergent in afinite interval does not yield the same asymptotic behavior as the underlying differentialequation. Therefore, it is very important to investigate the dynamics of numerical methodsfor solving delay differential equations.The purpose of this paper is to study some dynamical properties of θ-methods and mul-tistep methods solving delay differential equations. It contains1 numerical dissipativity of linear θ-method and multistep methods,2 regularity of linear multistep methods, and3 stability of spurious period two solution of linear θ-method.