Continuous block implicit hybrid one-step methods for ordinary and delay differential equations

DOI10.1016/j.apnum.2011.09.001zbMath1243.65087OpenAlexW2086478544MaRDI QIDQ651093

Quanhong Yu, Cilai Jin, Hong-Jiong Tian

Publication date: 8 December 2011

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2011.09.001

zbMATH Keywords

stabilityconvergencenumerical examplesordinary differential equationcontinuous extensiondelay differential equationsblock implicit hybrid one-step method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) 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)

Related Items

Continuous parallel block methods and their applications, Functionally-fitted block methods for second order ordinary differential equations, Functionally-fitted block \( \theta \)-methods for ordinary differential equations, An efficient computational algorithm for pricing European, barrier and American options, Functionally-fitted block methods for ordinary differential equations, Solving delay differential equations by the five-point one-step block method using Neville's interpolation

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical treatment of delay differential equations by Hermite interpolation
• Perturbed collocation and Runge-Kutta methods
• \(A\)-stable parallel block methods for ordinary and integro-differential equations
• Strong contractivity properties of numerical methods for ordinary and delay differential equations
• A new interpolation procedure for adapting Runge-Kutta methods to delay differential equations
• Stability Properties of Interpolants for Runge–Kutta Methods
• Continuous Block $\theta$-Methods for Ordinary and Delay Differential Equations
• Solving Ordinary Differential Equations I
• Natural Continuous Extensions of Runge-Kutta Methods
• Parallel Solution of ODE’<scp>s</scp> by Multiblock Methods
• A block method for the numerical integration of stiff systems of ordinary differential equations
• The stability of the block θ-methods
• Block Implicit One-Step Methods
• L-Stable Parallel One-Block Methods for Ordinary Differential Equations
• Interpolants for Runge-Kutta formulas
• The Numerical Integration of Neutral Functional‐Differential Equations by Fully Implicit One‐Step Methods
• Block Implicit One-Step Methods
• A-stable block implicit one-step methods
• High order stiffly stable composite multistep methods for numerical integration of stiff differential equations
• Natural spline block implicit methods