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2003•Acta Scientiarum Naturalium Universitatis SunyatseniRequires access

DELAY-DEPENDENT TREATMENT OF LINEAR MULTISTEP METHODS FOR NEUTRAL DELAY DIFFERENTIAL EQUATIONS

SyedKhalidJaffer, Ming-zhuLiu

Open publisher page 3 citations

Abstract

This paper deals with a delay-dependent treatment of linear multistep methods for neutral delay differential equations y'(t) = ay(t) + by(t - τ) + cy'(t -τ ), t > 0, y(t) =g(t), -τ ≤ t ≤0, a,b andc ∈ R. The necessary condition for linear multistep methods to be Nτ(0)-stable is given. It is shown that the trapezoidal rule is Nτ-(0)-compatible. Figures of stability region for some linear multistep methods are depicted.

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What this paper is about

This paper deals with a delay-dependent treatment of linear multistep methods for neutral delay differential equations y'(t) = ay(t) + by(t - τ) + cy'(t -τ ), t > 0, y(t) =g(t), -τ ≤ t ≤0, a,b andc ∈ R. The necessary condition for linear multistep methods to be Nτ(0)-stable is given. It is shown that the trapezoidal rule is Nτ-(0)-compatible. Figures of stability region for some linear multistep methods are depicted.

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Available abstract

This paper deals with a delay-dependent treatment of linear multistep methods for neutral delay differential equations y'(t) = ay(t) + by(t - τ) + cy'(t -τ ), t > 0, y(t) =g(t), -τ ≤ t ≤0, a,b andc ∈ R. The necessary condition for linear multistep methods to be Nτ(0)-stable is given. It is shown that the trapezoidal rule is Nτ-(0)-compatible. Figures of stability region for some linear multistep methods are depicted.

Key concepts: Linear multistep method, Delay differential equation, Mathematics, Backward differentiation formula, Stability (learning theory), Applied mathematics, Control theory (sociology), Differential equation

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