A criterion for \(P\)-stability properties of Runge-Kutta methods

DOI10.1007/BF02510412zbMath0917.65074MaRDI QIDQ1279699

K. Appert

Publication date: 25 July 1999

Published in: BIT (Search for Journal in Brave)

zbMATH Keywords

delay differential equationsRunge-Kutta methods\(A\)-stability\(P\)-stability

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) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) General theory of functional-differential equations (34K05)

Related Items (3)

Method of lines approximations of delay differential equations ⋮ Conditional contractivity of Runge-Kutta methods for nonlinear differential equations with many variable delays ⋮ Stability analysis of two-step Runge-Kutta methods for delay differential equations

Cites Work

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• P-stable and P[\(\alpha\),\(\beta\)-stable integration/interpolation methods in the solution of retarded differential-difference equations]
• P-stability properties of Runge-Kutta methods for delay differential equations
• The stability of natural Runge-Kutta methods for nonlinear delay differential equations
• NP-stability of Runge-Kutta methods based on classical quadrature
• Natural Continuous Extensions of Runge-Kutta Methods
• Efficiently Implementable Algebraically Stable Runge–Kutta Methods
• Special stability problems for functional differential equations
• Diagonally Implicit Runge–Kutta Methods for Stiff O.D.E.’s
• A special family of Runge-Kutta methods for solving stiff differential equations

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