A stability property of \(A\)-stable collocation-based Runge-Kutta methods for neutral delay differential equations

DOI10.1007/BF01733796zbMath0870.65070MaRDI QIDQ2565279

Toshiyuki Koto

Publication date: 11 March 1997

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

stabilityasymptotic stabilityRunge-Kutta methods\(A\)-stabilitycollocationneutral delay differential equations\(A\)-stable methodschoice of stepsize

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) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (11)

NP-stability of Runge-Kutta methods based on classical quadrature ⋮ Stability analysis of general linear methods for nonlinear neutral delay differential equations ⋮ Stability analysis of numerical methods for systems of functional-differential and functional equations. ⋮ Stability of Runge-Kutta methods for neutral delay differential equations ⋮ Dissipativity of \(\theta \)-methods for a class of nonlinear neutral delay differential equations ⋮ Asymptotic stability of Rosenbrock methods for systems of functional differential and functional equations ⋮ Stability analysis of one-leg methods for nonlinear functional differential and functional equations ⋮ Stability of the Radau IA and Lobatto IIIC methods for neutral delay differential system ⋮ Retarded differential equations ⋮ Stability analysis of Runge-Kutta methods for nonlinear functional differential and functional equations ⋮ Stability of Runge-Kutta methods for delay integro-differential equations

Cites Work

• Stability in linear delay equations
• P-stability properties of Runge-Kutta methods for delay differential equations
• Stability analysis of one-step methods for neutral delay-differential equations
• Natural Runge-Kutta and projection methods
• Introduction to functional differential equations
• A stability property of \(A\)-stable natural Runge-Kutta methods for systems of delay differential equations
• One-Step Methods of any Order for Neutral Functional Differential Equations
• Natural Continuous Extensions of Runge-Kutta Methods

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