The order of B-convergence of algebraically stable Runge-Kutta methods

DOI10.1007/BF01937355zbMath0629.65075OpenAlexW2123462197MaRDI QIDQ1094105

Willem H. Hundsdorfer, Kevin Burrage

Publication date: 1987

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01937355

zbMATH Keywords

implicit Runge-Kutta methodsstage ordersemilinear problemsstiff initial value problemsnonlinear dissipative problemsoptimal B-convergence

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (13)

Error of Runge-Kutta methods for stiff problems studied via differential algebraic equations ⋮ The dichotomy of stiffness: Pragmatism versus theory ⋮ Stability and convergence at the PDE/stiff ODE interface ⋮ B-convergence: A survey ⋮ Efficiently implementable multivalue methods for solving stiff ordinary differential equations ⋮ B-convergence of general linear methods for stiff problems. ⋮ Stability and B-convergence of general linear methods ⋮ Numerical integration of Hamiltonian problems by G-symplectic methods ⋮ Nonlinear Stability and B-convergence of Additive Runge-Kutta Methods for Nonlinear Stiff Problems ⋮ \(D\)-convergence of general linear methods for stiff delay differential equations ⋮ A new approach to optimal B-convergence ⋮ Runge-Kutta Methods for Partial Differential Equations and Fractional Orders of Convergence ⋮ An algebraic characterization of B-convergent Runge-Kutta methods

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Feasibility and contractivity in implicit Runge-Kutta methods
• A study of B-convergence of Runge-Kutta methods
• B-convergence of the implicit midpoint rule and the trapezoidal rule
• 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
• Non-linear stability of a general class of differential equation methods
• Efficiently Implementable Algebraically Stable Runge–Kutta Methods
• A special family of Runge-Kutta methods for solving stiff differential equations
• Stability Criteria for Implicit Runge–Kutta Methods
• High order algebraically stable Runge-Kutta methods

This page was built for publication: The order of B-convergence of algebraically stable Runge-Kutta methods