General linear methods with external stages of different orders

DOI10.1007/BF01733788zbMath0905.65086OpenAlexW2033249766MaRDI QIDQ2565271

Zdzisław Jackiewicz, Rossana Vermiglio

Publication date: 11 March 1997

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01733788

zbMATH Keywords

numerical exampleserror estimationorder conditionsdiagonally implicit multistage integration methodsgeneral linear methodstwo-step Runge-Kutta methods

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) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items

Construction and implementation of general linear methods for ordinary differential equations: a review, Strong stability preserving general linear methods, Construction of two-step Runge--Kutta methods with large regions of absolute stability, Implementation of second derivative general linear methods, An alternative approach for order conditions of Runge-Kutta-Nyström methods, Order conditions for general linear methods, Derivation and implementation of two-step Runge-Kutta pairs, Order conditions for Volterra Runge-Kutta methods, Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations, Construction of two-step Runge-Kutta methods of high order of ordinary differential equations, Order conditions for partitioned Runge-Kutta methods., Strong stability preserving second derivative general linear methods, STRONG STABILITY PRESERVING MULTISTAGE INTEGRATION METHODS, Stability analysis of two-step Runge-Kutta methods for delay differential equations, Implementation of DIMSIMs for stiff differential systems

Cites Work

• Unnamed Item
• 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
• Variable stepsize diagonally implicit multistage integration methods for ordinary differential equations
• 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