Numerical dissipativity of multistep methods for delay differential equations

DOI10.1016/j.amc.2006.10.048zbMath1123.65073OpenAlexW2035423204MaRDI QIDQ2371506

Liqiang Fan, Hong-Jiong Tian, Jia-Xiang Xiang

Publication date: 4 July 2007

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

Full work available at URL: https://doi.org/10.1016/j.amc.2006.10.048

zbMATH Keywords

numerical exampledynamical systemsdissipativityA-stabilitylinear multistep methodsabsorbing setone-leg methoddissipative delay differential equations

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (11)

Dissipativity of variable-stepsize Runge-Kutta methods for nonlinear functional differential equations with application to Nicholson's blowflies models ⋮ Dissipativity of extended Pouzet–Runge–Kutta methods for neutral delay integro-differential equations ⋮ New generalized Halanay inequalities and relative applications to neural networks with variable delays ⋮ Generalized Halanay inequalities for dissipativity of Volterra functional differential equations ⋮ Dissipativity of θ-methods for a class of nonlinear neutral delay integro-differential equations ⋮ Stability in mean for uncertain delay differential equations based on new Lipschitz conditions ⋮ Numerical dissipativity of neutral integro-differential equations with delay ⋮ Dissipativity of one-leg methods for neutral delay integro-differential equations ⋮ Asymptotic stability, contractivity and dissipativity of one-leg \(\theta \)-method for non-autonomous delay functional differential equations ⋮ Dissipativity of delay functional differential equations with bounded lag ⋮ Delay-dependent dissipativity of nonlinear delay differential equations

Cites Work

• Unnamed Item
• Introduction to functional differential equations
• Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems
• NUMERICAL AND ANALYTIC DISSIPATIVITY OF THE θ-METHOD FOR DELAY DIFFERENTIAL EQUATIONS WITH A BOUNDED VARIABLE LAG
• Dissipativity of Runge-Kutta methods for dynamical systems with delays

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