Variable stepsize diagonally implicit multistage integration methods for ordinary differential equations

DOI10.1016/0168-9274(94)00057-NzbMath0822.65049MaRDI QIDQ1347141

Rossana Vermiglio, Marino Zennaro, Zdzisław Jackiewicz

Publication date: 15 October 1995

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

zbMATH Keywords

stabilitynumerical examplestiff systemsparallel computingorder conditionsgeneral linear methodsvariable step sizeNordsieck techniqueButcher's diagonally implicit multistage integration 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) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

A nonlinear optimization approach to the construction of general linear methods of high order ⋮ Construction and implementation of general linear methods for ordinary differential equations: a review ⋮ Variable stepsize SDIMSIMs for ordinary differential equations ⋮ Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations ⋮ General linear methods with external stages of different orders ⋮ On the numerical approximation of trajectories in the phase plane

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Numerical treatment of O.D.Es.: The theory of A-methods
• Diagonally-implicit multi-stage integration methods
• Diagonally implicit general linear methods for ordinary differential equations
• Elements of a general theory of composite integration methods
• Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations
• A New Theoretical Approach to Runge–Kutta Methods
• A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations

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