Numerical dissipativity of multistep methods for delay differential equations

Dissipative differential equations have frequently appeared in the fields of physics, engineering, and biology. In this paper we investigate numerical dissipativity of linear multistep and one-leg methods applied to a class of dissipative delay differential equations. We show that for such class of dissipative systems these numerical methods are dissipative if and only if they are A-stable for ordinary differential equations. One numerical experiment is given to illustrate our result.