Interpolating Runge-Kutta methods for vanishing delay differential equations

DOI10.1007/BF02238433zbMath0843.65052OpenAlexW1590412594MaRDI QIDQ1900694

Min Hu, W. H. Enright

Publication date: 15 August 1996

Published in: Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02238433

zbMATH Keywords

algorithmtest problemsvanishing delaycontinuous Runge-Kutta codesdifferential delay problems

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 (7)

A mixed finite element for the Stokes problem using quadrilateral elements ⋮ Issues in the numerical solution of evolutionary delay differential equations ⋮ Interpolating Runge-Kutta methods for vanishing delay differential equations ⋮ Variable-step variable-order 3-stage Hermite-Birkhoff-Obrechkoff DDE solver of order 4 to 14 ⋮ Runge-Kutta research at Toronto ⋮ DDVSS6 ⋮ Solving delay differential equations of small and vanishing lag using multistep block method

Uses Software

• dverk
• SYSDEL
• DDRK6N

Cites Work

• A new error-control for initial value solvers
• Developing a delay differential equation solver
• A fifth-order interpolant for the Dormand and Prince Runge-Kutta method
• Interpolating Runge-Kutta methods for vanishing delay differential equations
• A numerical method for vanishing-lag delay differential equations
• The Relative Efficiency of Alternative Defect Control Schemes for High-Order Continuous Runge–Kutta Formulas
• Differentiable Interpolants for High-Order Runge–Kutta Methods
• Derivation of Efficient, Continuous, Explicit Runge–Kutta Methods
• Automatic Integration of Functional Differential Equations: An Approach
• Interpolants for Runge-Kutta formulas
• Fourth- and Fifth-Order, Scaled Rungs–Kutta Algorithms for Treating Dense Output
• One-Step Methods for the Numerical Solution of Volterra Functional Differential Equations

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