Abstract
This paper is concerned with asymptotic stability property of linear θ-method for partial functional differential equations with delay. A sufficient condition for the underlying partial functional differential equations to be asymptotically stable is presented. We investigate numerical stability of the linear θ-method by using the spectral radius condition. When θ ∈ [0, 1/2), a sufficient and necessary condition for the linear θ-method to be asymptotically stable is established. When θ ∈ [1/2, 1], the linear θ-method is unconditionally asymptotically stable. The behaviour of the norm of the iteration matrix when the linear θ-method is asymptotically stable is studied by using Kreiss resolvent condition. Numerical experiments have been implemented to confirm the derived stability properties of the numerical method.
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