On stability sets for numerical discretizations of neutral delay differential equations

Abstract

The paper discusses the -method discretization of the neutral delay differential equation y'(t) = ay (t) + by (t - τ) + cy' (t - τ), t > 0, where a, b, c are real constant coefficients and is a positive real lag. Using recent developments on stability of appropriate delay difference equations we give a complete description of stability sets for this discretization. Some of their properties and related comparisons with the stability set for the underlying neutral differential equation are discussed as well.