Constructive characterization of A-stable approximations to exp(z) and its connection with algebraically stable Runge-Kutta methods

DOI10.1007/BF01408698zbMath0493.65035MaRDI QIDQ1168692

Ernst Hairer

Publication date: 1982

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

Full work available at URL: https://eudml.org/doc/132795

zbMATH Keywords

exponential functionimplicit Runge-Kutta methodsrational approximationsalgebraic stabilityI-stabilityA- stabilitytheory of order stars

Mathematics Subject Classification ID

Approximation by rational functions (41A20) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (6)

Stability of implicit Runge-Kutta methods for nonlinear stiff differential equations ⋮ Adaptive Nyström-Runge-Kutta-Methoden für gewöhnliche Differentialgleichungssysteme zweiter Ordnung ⋮ The role of orthogonal polynomials in numerical ordinary differential equations ⋮ On the stability of spline-collocation methods of multivalue type ⋮ A- and B-stability for Runge-Kutta methods - characterizations and equivalence ⋮ The equivalence of B-stability and A-stability

Cites Work

• Unnamed Item
• Sur la B-stabilité des méthodes de Runge-Kutta
• Stability of explicit time discretizations for solving initial value problems
• Algebraically Stable and Implementable Runge-Kutta Methods of High Order
• Order stars and stability theorems
• Characterization of allA-stable methods of order 2m-4
• A stability property of implicit Runge-Kutta methods
• Stability Criteria for Implicit Runge–Kutta Methods

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