Numerical stability of the \(\theta\)-methods for systems of differential equations with several delay terms

DOI10.1016/0377-0427(91)90090-7zbMath0731.65072OpenAlexW1965833286MaRDI QIDQ808193

Lianhua Lu

Publication date: 1991

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0377-0427(91)90090-7

zbMATH Keywords

asymptotic stabilitydelay differential equationstheta methodGP-stability

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) General theory of functional-differential equations (34K05)

Related Items (14)

Continuous parallel block methods and their applications ⋮ \(\mathcal H\)-stability of linear \(\theta\)-method with general variable stepsize for system of pantograph equations with two delay terms ⋮ Numerical stability analysis of numerical methods for Volterra integral equations with delay argument ⋮ Interface stabilization of a parabolic-hyperbolic PDE system with delay in the interaction ⋮ A novel mathematical model of heterogeneous cell proliferation ⋮ Numerical radius for the asymptotic stability of delay differential equations ⋮ Stability of \(\vartheta\)-methods for delay integro-differential equations. ⋮ \(\mathcal H\)-stability of Runge-Kutta methods with general variable stepsize for pantograph equation. ⋮ Stability analysis for linear delay differential equations and numerical examples ⋮ GP\(_G\)-stability of Runge-Kutta methods for generalized delay differential systems ⋮ Stability analysis for delay differential equations with multidelays and numerical examples ⋮ The numerical stability of multistep methods for Volterra integral equations with many delays ⋮ Stability estimates of difference schemes for neutral delay differential equations ⋮ Development and application of Halanay-type theory: Evolutionary differential and difference equations with time lag

Cites Work

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• Stability in linear multistep methods for pure delay equations
• Stability properties of numerical methods for solving delay differential equations
• P-stability properties of Runge-Kutta methods for delay differential equations
• On the asymptotic stability of \(\theta\)-methods for delay differential equations
• The Stability of the θ-methods in the Numerical Solution of Delay Differential Equations
• The Stability of Difference Formulas for Delay Differential Equations
• Special stability problems for functional differential equations
• Highly Stable Multistep Methods for Retarded Differential Equations

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