Applications of order arrows

DOI10.1016/j.apnum.2012.01.002zbMath1241.65070OpenAlexW2040994147MaRDI QIDQ413623

Ali Abdi, John C. Butcher

Publication date: 7 May 2012

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2012.01.002

zbMATH Keywords

numerical examplesA-stabilityorder starsrational approximationsorder arrowsorder barriers

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 (5)

Construction of high-order quadratically stable second-derivative general linear methods for the numerical integration of stiff ODEs ⋮ Implementation of second derivative general linear methods ⋮ On the construction of second derivative diagonally implicit multistage integration methods for ODEs ⋮ Order conditions for second derivative general linear methods ⋮ Implementation of Nordsieck second derivative methods for stiff ODEs

Cites Work

• Unnamed Item
• Order bounds for second derivative approximations
• Generalized Padé approximations to the exponential function
• Order and stability of generalized Padé approximations
• The \(A\)-stability of methods with Padé and generalized Padé stability functions
• Order stars and stability theorems
• The Order of Numerical Methods for Ordinary Differential Equations
• General linear methods

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