The stability of natural Runge-Kutta methods for nonlinear delay differential equations

DOI10.1007/BF03167314zbMath0887.65093MaRDI QIDQ1365321

Toshiyuki Koto

Publication date: 25 May 1998

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Lyapunov functionalsdelay differential equationsRunge-Kutta methods\(A\)-stabilityalgebraic 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 (4)

Contractivity properties of a class of linear multistep methods for nonlinear neutral delay differential equations ⋮ Method of lines approximations of delay differential equations ⋮ A criterion for \(P\)-stability properties of Runge-Kutta methods ⋮ Retarded differential equations

Cites Work

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• Natural Continuous Extensions of Runge-Kutta Methods
• Special stability problems for functional differential equations
• Complete Algebraic Characterization of A-Stable Runge–Kutta Methods
• Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems

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