Numerical stability of the θ-methods for systems of differential equations with several delay terms

摘要

Consider the following two-dimensional delay differential equation (DDE) with the initial conditions , where aj, bj ϵ , dj > 0, and u0(t),ν0(t) are continuous and complex valued. The author give the sufficient conditions for the asymptotic stability of equation (0.1). The numerical stabilities of the linear θ-method and the one-leg θ-method are investigated by analysing their stabilities behaviour in the solutions of (0.1). It is shown that the linear θ-method is GP-stable if and only if ⩽θ⩽ 1 and that the one-leg θ-method is GP-stable if and only if θ = 1.