Starting procedures for general linear methods

DOI10.1016/j.apnum.2017.05.009zbMath1370.65034OpenAlexW2734861480MaRDI QIDQ2012626

Giuseppe Izzo, Zdzisław Jackiewicz, Giovanna Califano

Publication date: 1 August 2017

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2017.05.009

zbMATH Keywords

order conditionsgeneral linear methodsgeneralized Runge-Kutta methodsstarting procedures

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (15)

Error propagation for implicit-explicit general linear methods ⋮ Strong stability preserving transformed DIMSIMs ⋮ Construction of \(G\)- or \(G (\epsilon)\)-symplectic general linear methods ⋮ Strong stability preserving general linear methods with Runge-Kutta stability ⋮ Transformed implicit-explicit second derivative diagonally implicit multistage integration methods with strong stability preserving explicit part ⋮ Convergence results for implicit-explicit general linear methods ⋮ Alternating directions implicit integration in a general linear method framework ⋮ Strong stability preserving implicit-explicit transformed general linear methods ⋮ Starting procedures for general linear methods ⋮ A new class of strong stability preserving general linear methods ⋮ A new class of efficient general linear methods for ordinary differential equations ⋮ Transformed implicit-explicit DIMSIMs with strong stability preserving explicit part ⋮ Parallel implicit-explicit general linear methods ⋮ Strong stability preserving IMEX methods for partitioned systems of differential equations ⋮ A new class of \(G ( \epsilon )\)-symplectic general linear methods

Uses Software

• DIMSIM

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Two-step Runge-Kutta methods with quadratic stability functions
• Strong stability preserving general linear methods
• Diagonally-implicit multi-stage integration methods
• Construction of high order diagonally implicit multistage integration methods for ordinary differential equations
• Diagonally implicit general linear methods for ordinary differential equations
• Nordsieck representation of DIMSIMs
• The construction of practical general linear methods
• Implementation of DIMSIMs for stiff differential systems
• Construction of general linear methods with Runge-Kutta stability properties
• Explicit general linear methods with inherent Runge--Kutta stability
• Experiments with a variable-order type 1 DIMSIM code
• Starting procedures for general linear methods
• Improved starting methods for two-step Runge-Kutta methods of stage-order \(p\)-3
• Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations
• Starting methods for two-step Runge-Kutta methods of stage-order 3 and order 6
• Solving Ordinary Differential Equations I
• Non-linear stability of a general class of differential equation methods
• Derivation of Efficient, Continuous, Explicit Runge–Kutta Methods
• Implementation of Diagonally Implicit Multistage Integration Methods for Ordinary Differential Equations
• A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations
• STRONG STABILITY PRESERVING MULTISTAGE INTEGRATION METHODS
• Order Barriers for Continuous Explicit Runge-Kutta Methods
• General linear methods

This page was built for publication: Starting procedures for general linear methods