On the stability of adaptations of Runge-Kutta methods to systems of delay differential equations

DOI10.1016/S0168-9274(96)00035-9zbMath0867.65045OpenAlexW2021083294MaRDI QIDQ5961744

Karel J. in 't Hout

Publication date: 21 April 1997

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0168-9274(96)00035-9

zbMATH Keywords

interpolationstabilityRunge-Kutta methodssystems of delay 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) General theory of functional-differential equations (34K05)

Related Items (8)

Properties of analytic solution and numerical solution of multi-pantograph equation ⋮ On stability regions of the modified midpoint method for a linear delay differential equation ⋮ The stability of Radau IIA collocation processes for delay differential equations ⋮ Solving DDEs in Matlab ⋮ Variational iteration method for solving a generalized pantograph equation ⋮ Runge-Kutta methods for the multi-pantograph delay equation ⋮ Asymptotic stability of numerical methods for linear delay parabolic differential equations ⋮ Asymptotic stability analysis of the linear θ-method for linear parabolic differential equations with delay

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multistep natural continuous extensions of Runge-Kutta methods: The potential for stable interpolation
• Stability analysis of numerical methods for delay differential equations
• P-stable and P[\(\alpha\),\(\beta\)-stable integration/interpolation methods in the solution of retarded differential-difference equations]
• Singly-implicit Runge-Kutta methods for retarded and ordinary differential equations
• P-stability properties of Runge-Kutta methods for delay differential equations
• Numerical treatment of delay differential equations by Hermite interpolation
• The stability of a class of Runge-Kutta methods for delay differential equations
• A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
• A stability property of \(A\)-stable natural Runge-Kutta methods for systems of delay differential equations
• Stability analysis of numerical methods for systems of neutral delay-differential equations
• On the numerical integration of a symmetric system of difference- differential equations of neutral type
• Stability analysis of Runge-Kutta methods for systems of delay differential equations
• Solving Ordinary Differential Equations I
• The Stability of the θ-methods in the Numerical Solution of Delay Differential Equations
• The Stability of Difference Formulas for Delay Differential Equations
• The Optimal Accuracy of Difference Schemes
• Natural Continuous Extensions of Runge-Kutta Methods
• Trigonometric Polynomials and Difference Methods of Maximum Accuracy
• Special stability problems for functional differential equations

This page was built for publication: On the stability of adaptations of Runge-Kutta methods to systems of delay differential equations