Stability and $B$-convergence properties of multistep Runge-Kutta methods

DOI10.1090/S0025-5718-99-01159-XzbMath0954.65067MaRDI QIDQ4501036

Shou-fu Li

Publication date: 3 September 2000

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

nonlinear stabilitymultistep Runge-Kutta methodsdiagonal stabilityalgebraic stabilityB-convergence

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 (11)

General linear and spectral Galerkin methods for the nonlinear two-sided space distributed-order diffusion equation ⋮ Nonlinear stability and convergence of two-step Runge-Kutta methods for Volterra delay integro-differential equations ⋮ A general class of linear unconditionally energy stable schemes for the gradient flows ⋮ B-convergence of general linear methods for stiff problems. ⋮ Symplectic properties of multistep Runge-Kutta methods. ⋮ Numerical dissipativity of neutral integro-differential equations with delay ⋮ Stability of multistep Runge-Kutta methods for systems of functional-differential and functional equations. ⋮ \(B\)-theory of general linear methods for Volterra functional differential equations ⋮ \(D\)-convergence of general linear methods for stiff delay differential equations ⋮ Hybrid BDF methods for the numerical solutions of ordinary differential equations ⋮ Nonlinear stability of general linear methods for neutral delay differential equations

Uses Software

• RODAS

Cites Work

• B-convergence of Lobatto IIIC formulas
• Modern convergence theory for stiff initial-value problems
• An extension of B-convergence for Runge-Kutta methods
• Extending convergence theory for nonlinear stiff problems. I
• A note on convergence concepts for stiff problems
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• High Order Algebraically Stable Multistep Runge–Kutta Methods
• Non-linear stability of a general class of differential equation methods
• The Concept of B-Convergence
• A stability property of implicit Runge-Kutta methods
• On the implementation of implicit Runge-Kutta methods
• B-Convergence Properties of Multistep Runge-Kutta Methods
• Unnamed Item
• Unnamed Item

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