On the uniform power-boundedness of a family of matrices and the applications to one-leg and linear multistep methods

DOI10.1007/BF01400914zbMath0526.65051MaRDI QIDQ594552

Germund Dahlquist, Mingyou Huang, Randall J. LeVeque

Publication date: 1983

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

Full work available at URL: https://eudml.org/doc/132857

zbMATH Keywords

stability setlinear multistep methodstest equationcompanion matricesone-leg methodresolvent criterionuniform power-boundedness

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

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Cites Work

• Unnamed Item
• Estimation of iterated matrices, with application to the von Neumann condition
• G-stability is equivalent toA-stability
• Über Die Stabilitätsdefinition Für Differenzengleichungen Die Partielle Differentialgleichungen Approximieren
• A new class of highly-stable methods:A 0-stable methods