Algebraic characterization of \(A\)-stable Runge-Kutta methods

DOI10.1016/0168-9274(89)90029-9zbMath0671.65074OpenAlexW2026347555MaRDI QIDQ1119361

H. Türke, Rudolf Scherer

Publication date: 1989

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-9274(89)90029-9

zbMATH Keywords

numerical examplesRunge-Kutta methods\(A\)-stability\(B\)-stabilityalgebraic characterization\(W\)-transformation\(A\)-stable methods

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)

Related Items (6)

Properties of Runge-Kutta-summation-by-parts methods ⋮ System theory for numerical analysis ⋮ Efficient A-stable peer two-step methods ⋮ An inverse eigenvalue problem: Computing \(B\)-stable Runge-Kutta methods having real poles ⋮ Non-minimal Runge-Kutta methods ⋮ Algebraic characterization of I-stable Runge-Kutta methods

Cites Work

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• The equivalence of B-stability and A-stability
• Algebraically Stable and Implementable Runge-Kutta Methods of High Order
• Characterization of allA-stable methods of order 2m-4
• OnA-stable implicit Runge-Kutta methods
• A System Theory Criterion for Positive Real Matrices
• On Nonnegative Solutions of the Equation $AD + DA' = - C$
• Implicit Runge-Kutta Processes

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