General linear methods for ordinary differential equations

DOI10.1016/j.matcom.2007.02.006zbMath1159.65333OpenAlexW2138301603MaRDI QIDQ1005678

John C. Butcher

Publication date: 9 March 2009

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2007.02.006

zbMATH Keywords

linear multistep methodsstiff differential equationsgeneral linear methodsinherent Runge-Kutta stabilityimplicit methods

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 (4)

Numerical solutions of Volterra integro-differential equations using general linear method ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

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• High order A-stable numerical methods for stiff problems
• An application of the Runge-Kutta space
• General linear method: A survey
• On the Butcher group and general multi-value methods
• General linear methods: Connection to one step methods and invariant curves
• A generalization of singly-implicit Runge-Kutta methods
• A new approach to error estimation for general linear methods
• The construction of practical general linear methods
• Construction of general linear methods with Runge-Kutta stability properties
• A transformation relating explicit and diagonally-implicit general linear methods
• Error estimation for Nordsieck methods
• Explicit general linear methods with inherent Runge--Kutta stability
• On error estimation in general linear methods for stiff ODEs
• On Numerical Integration of Ordinary Differential Equations
• Implementation of Diagonally Implicit Multistage Integration Methods for Ordinary Differential Equations
• The Order of Numerical Methods for Ordinary Differential Equations
• On the Convergence of Numerical Solutions to Ordinary Differential Equations
• The Numerical Integration of Ordinary Differential Equations
• An Algebraic Theory of Integration Methods
• General linear methods
• General linear methods
• General linear methods for stiff differential equations
• A reliable error estimation for diagonally implicit multistage integration methods

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