On the relation between algebraic stability and B-convergence for Runge- Kutta methods

DOI10.1007/BF01386409zbMath0702.65079OpenAlexW1983257177MaRDI QIDQ915398

J. F. B. M. Kraaijevanger, Josef Schneid, Kees Dekker

Publication date: 1990

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133447

zbMATH Keywords

stage orderstability functionalgebraic stabilityB-convergencealgebraically stable Runge-Kutta method

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)

Related Items (5)

Properties of Runge-Kutta-summation-by-parts methods ⋮ The dichotomy of stiffness: Pragmatism versus theory ⋮ B-convergence of general linear methods for stiff problems. ⋮ On the positivity step size threshold of Runge--Kutta methods ⋮ Runge-Kutta methods: Some historical notes

Cites Work

• Unnamed Item
• Unnamed Item
• A new approach to optimal B-convergence
• B-convergence of Lobatto IIIC formulas
• Error bounds for the solution to the algebraic equations in Runge-Kutta methods
• Feasibility and contractivity in implicit Runge-Kutta methods
• B-convergence of the implicit midpoint rule and the trapezoidal rule
• On the maximum order of optimal B-convergence of Lobatto III C schemes
• On the solvability of the systems of equations arising in implicit Runge- Kutta methods
• Sur la B-stabilité des méthodes de Runge-Kutta
• On the existence of solutions to the algebraic equations in implicit Runge-Kutta methods
• Reducibility and contractivity of Runge-Kutta methods revisited
• Stability Properties of Implicit Runge–Kutta Methods
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• The Concept of B-Convergence
• Stability Criteria for Implicit Runge–Kutta Methods

This page was built for publication: On the relation between algebraic stability and B-convergence for Runge- Kutta methods