Equilibrium states of adaptive algorithms for delay differential equations

DOI10.1016/0377-0427(93)E0268-QzbMath0833.65070OpenAlexW2006378515MaRDI QIDQ1899949

Desmond J. Higham, Ioannis Th. Famelis

Publication date: 11 October 1995

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(93)e0268-q

zbMATH Keywords

delay differential equationerror controladaptive algorithmsRunge- Kutta methodslow order methods

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

Related Items (3)

Existence and stability of fixed points for a discretised nonlinear reaction-diffusion equation with delay ⋮ Dynamics of constant and variable stepsize methods for a nonlinear population model with delay ⋮ Neural network solution of single-delay differential equations

Cites Work

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• The Stability of the θ-methods in the Numerical Solution of Delay Differential Equations
• Equilibrium states of Runge Kutta schemes
• Equilibrium states of Runge-Kutta schemes: part II
• Analysis of Stepsize Selection Schemes for Runge-Kutta Codes
• Analysis of Error Control Strategies for Continuous Runge–Kutta Methods
• Derivation of Efficient, Continuous, Explicit Runge–Kutta Methods
• Computing stability regions—Runge-Kutta methods for delay differential equations
• Control theoretic techniques for stepsize selection in explicit Runge-Kutta methods

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