The asymptotic stability of theoretical and numerical solutions for systems of neutral multidelay-differential equations

DOI10.1007/BF02871977zbMath0924.65079MaRDI QIDQ1286638

S. Z. Zhou, Cheng-Jian Zhang

Publication date: 16 November 1999

Published in: Science in China. Series A (Search for Journal in Brave)

zbMATH Keywords

asymptotic stability\(A\)-stabilitymultistep Runge-Kutta methodsystems of neutral multidelay-differential equations

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Neutral functional-differential equations (34K40) Numerical investigation of stability of solutions to ordinary differential equations (65L07) Asymptotic properties of solutions to ordinary differential equations (34D05)

Related Items (23)

Solving semi-linear stiff neutral equations by implicit–explicit Runge-Kutta methods ⋮ Strang-type preconditioners applied to ordinary and neutral differential-algebraic equations ⋮ An extension of numerical stability criteria for linear neutral multidelay-integro-differential equations ⋮ Stability analysis of general linear methods for nonlinear neutral delay differential equations ⋮ Numerical approximation to semi-linear stiff neutral equations via implicit-explicit general linear methods ⋮ Stability analysis of linear multistep and Runge-Kutta methods for neutral multidelay-differential-algebraic systems ⋮ Long time behavior of non-Fickian delay reaction-diffusion equations ⋮ Stability analysis of numerical methods for systems of functional-differential and functional equations. ⋮ Asymptotic stability of exact and discrete solutions for neutral multidelay-integro-differential equations ⋮ Stability analysis of LMMs for systems of neutral multidelay-differential equations ⋮ Stability of exact and discrete energy for non-Fickian reaction-diffusion equations with a variable delay ⋮ Stability criteria for exact and discrete solutions of neutral multidelay-integro-differential equations ⋮ Asymptotic stability of Rosenbrock methods for systems of functional differential and functional equations ⋮ On the one-leg methods for solving nonlinear neutral differential equations with variable delay ⋮ LDG method for reaction-diffusion dynamical systems with time delay ⋮ NGP(\(\alpha\))-stability of general linear methods for NDDEs ⋮ Asymptotic behavior of multistep Runge-Kutta methods for systems of delay differential equations ⋮ Linear stability of general linear methods for systems of neutral delay differential equations ⋮ Dissipativity of \(\theta \)-methods for nonlinear delay differential equations of neutral type ⋮ Numerical stability of one-leg methods for neutral delay differential equations ⋮ The asymptotic stability of multistep multiderivative methods for systems of delay differential equations ⋮ Implicit-explicit one-leg methods for nonlinear stiff neutral equations ⋮ Stability analysis of Runge-Kutta methods for nonlinear functional differential and functional equations

Cites Work

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• Introduction to functional differential equations
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• Stability analysis of Runge-Kutta methods for systems of delay differential equations
• The Stability of the θ-methods in the Numerical Solution of Delay Differential Equations
• Special stability problems for functional differential equations
• B-Convergence Properties of Multistep Runge-Kutta Methods

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