Order bounds for second derivative approximations

DOI10.1007/s10543-011-0361-1zbMath1247.65103OpenAlexW2014225767MaRDI QIDQ438733

John C. Butcher, Ali Abdi

Publication date: 31 July 2012

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-011-0361-1

zbMATH Keywords

stabilitynumerical examplesA-stabilityRunge-Kutta methodrational approximationssecond derivative methodsorder 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 (10)

Construction of high-order quadratically stable second-derivative general linear methods for the numerical integration of stiff ODEs ⋮ Efficient Nordsieck second derivative general linear methods: construction and implementation ⋮ EXPLICIT NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS FOR ODES ⋮ Applications of order arrows ⋮ 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 ⋮ Construction of the Nordsieck second derivative methods with RK stability for stiff ODEs ⋮ Multivalue second derivative collocation methods ⋮ Implementation of Nordsieck second derivative methods for stiff ODEs

Uses Software

• RODAS

Cites Work

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• An extension of general linear methods
• Generalized Padé approximations to the exponential function
• Maximal order for second derivative general linear methods with Runge-Kutta stability
• On explicit two-derivative Runge-Kutta methods
• Order and stability of generalized Padé approximations
• The \(A\)-stability of methods with Padé and generalized Padé stability functions
• Second derivative methods with RK stability
• The real-pole sandwich for rational approximations and oscillation equations
• Attainable order of rational approximations to the exponential function with only real poles
• Restricted Padé Approximations to the Exponential Function

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