Vienna contributions to the development of RK-methods

DOI10.1016/S0168-9274(96)00024-4zbMath0870.65062MaRDI QIDQ5961732

Reinhard Frank, Winfried Auzinger, Hans J. Stetter

Publication date: 17 September 1997

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

zbMATH Keywords

convergencestiff systemsRunge-Kutta methodsdefect correctionTechnical University of Vienna

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Development of contemporary mathematics (01A65) 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) History of mathematics at specific universities (01A73) History of numerical analysis (65-03) Multiple scale methods for ordinary differential equations (34E13)

Related Items

A NOTE ON LYAPUNOV TRANSFORMATION AND EXPONENTIAL DECAY IN LINEAR ODE SYSTEMS ⋮ Beyond conventional Runge-Kutta methods in numerical integration of ODEs and DAEs by use of structures and local models ⋮ Extending convergence of BDF methods for a class of nonlinear strongly stiff problems

Uses Software

• RODAS
• NSDTST
• STDTST

Cites Work

• B-convergence of Lobatto IIIC formulas
• On error structures and extrapolation for stiff systems, with application in the method of lines
• On the unique solvability of the Runge-Kutta equations
• On the maximum order of optimal B-convergence of Lobatto III C schemes
• Extrapolation at stiff differential equations
• Sur la B-stabilité des méthodes de Runge-Kutta
• An extension of B-convergence for Runge-Kutta methods
• On the estimation of errors propagated in the numerical integration of ordinary differential equations
• The method of iterated defect-correction and its application to two-point boundary value problems. I
• The defect correction principle and discretization methods
• The method of iterated defect-correction and its application to two-point boundary value problems. II
• Iterated defect correction for differential equations. I: Theoretical results
• An algebraic characterization of B-convergent Runge-Kutta methods
• Asymptotic error expansions for stiff equations: Applications
• Asymptotic error expansions for stiff equations: An analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case
• Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type. I: RK- methods
• Asymptotic expansions for the error of discretization algorithms for non- linear functional equations
• Symmetric two-step algorithms for ordinary differential equations
• Extending convergence theory for nonlinear stiff problems. I
• Fehlerabschätzungen und Extrapolation mit rationalen Funktionen bei Verfahren vom Richardson-Typus
• A note on convergence concepts for stiff problems
• Stability Properties of Implicit Runge–Kutta Methods
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• The Concept of B-Convergence
• On the Stability and Accuracy of One-Step Methods for Solving Stiff Systems of Ordinary Differential Equations
• A stability property of implicit Runge-Kutta methods
• Iterated defect correction for the efficient solution of stiff systems of ordinary differential equations
• Stability Criteria for Implicit Runge–Kutta Methods
• Asymptotic Error Expansions for Stiff Equations: The Implicit Euler Scheme
• Two FORTRAN packages for assessing initial value methods
• On Extrapolation Algorithms for Ordinary Initial Value Problems
• A Study of Strong and Weak Stability in Discretization Algorithms
• Local Estimation of the Global Discretization Error
• A special stability problem for linear multistep methods
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