Two-step Runge-Kutta methods with quadratic stability functions

DOI10.1007/s10915-010-9378-xzbMath1203.65107OpenAlexW2152265807MaRDI QIDQ618601

Dajana Conte, Raffaele D'Ambrosio, Zdzisław Jackiewicz

Publication date: 16 January 2011

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-010-9378-x

zbMATH Keywords

absolute stability\(A\)-stabilityorder conditionstwo-step Runge-Kutta methods\(L\)-stabilityquadratic stability polynomials

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (19)

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Uses Software

• RODAS

Cites Work

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• Local error estimation for singly-implicit formulas by two-step Runge- Kutta methods
• Derivation and implementation of two-step Runge-Kutta pairs
• Derivation of continuous explicit two-step Runge-Kutta methods of order three
• Diagonally-implicit multi-stage integration methods
• Construction of two-step Runge-Kutta methods of high order of ordinary differential equations
• Construction of high order diagonally implicit multistage integration methods for ordinary differential equations
• Order conditions for two-step Runge-Kutta methods
• Construction of two-step Runge--Kutta methods with large regions of absolute stability
• The construction of practical general linear methods
• Two-step Runge-Kutta: Theory and practice
• Nordsieck representation of two-step Runge-Kutta methods for ordinary differential equations
• Variable stepsize continuous two-step Runge-Kutta methods for ordinary differential equations
• A transformation relating explicit and diagonally-implicit general linear methods
• Explicit general linear methods with inherent Runge--Kutta stability
• Applications of doubly companion matrices
• A Transformed implicit Runge-Kutta Method
• An implementation of singly-implicit Runge-Kutta methods
• A special family of Runge-Kutta methods for solving stiff differential equations
• Order Conditions for General Two-Step Runge--Kutta Methods
• A General Class of Two-Step Runge–Kutta Methods for Ordinary Differential Equations
• Implementation of two-step Runge-Kutta methods for ordinary differential equations

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