On stability sets for numerical discretizations of neutral delay differential equations

Abstract

The paper discusses the -method discretization of the neutral
delay dierential equation
y´(t) = a y(t) + b y(t-\tau) + c y´(t-\tau),    t > 0,
where a, b, c are real constant coecients and is a positive real lag. Using re-
cent developments on stability of appropriate delay dierence equations we give
a complete description of stability sets for this discretization. Some of their prop-
erties and related comparisons with the stability set for the underlying neutral
dierential equation are discussed as well.