Abstract:

Linear θ-methods are adapted for solving a class D(α,β₁,β₂,β3,γ,δ) of nonlinear neutral delay integro-differential equations (NDIDEs). It is proved that an A-stable linear θ-method (i.e. 1／2≤θ≤1) can preserve the asymptotic stability of the underlying systems of NDIDEs. A numerical test isgiven, which confirms the theoretical results in the end.

Key words: neutral delay integro-differential equations; linearθ-methods; asymptotic stability