Nonlinear stability of Runge-Kutta methods applied to infinite-delay-differential equations

DOI10.1016/S0895-7177(04)90520-1zbMath1068.65106OpenAlexW1992147499MaRDI QIDQ1765016

Geng Sun, Cheng-Jian Zhang

Publication date: 22 February 2005

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0895-7177(04)90520-1

zbMATH Keywords

asymptotic stabilityRunge-Kutta methodinfinite delay-differential equation

Mathematics Subject Classification ID

Related Items (14)

High order stable Runge-Kutta methods for nonlinear generalized pantograph equations on the geometric mesh ⋮ Laguerre approach for solving pantograph-type Volterra integro-differential equations ⋮ \(H_{\alpha}\)-stability of modified Runge-Kutta methods for nonlinear neutral pantograph equations ⋮ Fully-geometric mesh one-leg methods for the generalized pantograph equation: approximating Lyapunov functional and asymptotic contractivity ⋮ A new method based on the RKHSM for solving systems of nonlinear IDDes with proportional delays ⋮ An efficient IMEX method for nonlinear functional differential equations with state-dependent delay ⋮ Nonlinear stability and D-convergence of additive Runge-Kutta methods for multidelay-integro-differential equations ⋮ Analytic solutions to a class of nonlinear infinite-delay-differential equations ⋮ \(L^\infty\) error estimates of discontinuous Galerkin methods for delay differential equations ⋮ On \(A\)-stable one-leg methods for solving nonlinear Volterra functional differential equations ⋮ Generalized polynomial chaos for nonlinear random pantograph equations ⋮ Nonlinear stability of Runge-Kutta methods for neutral delay differential equations ⋮ Recent advances in the numerical analysis of Volterra functional differential equations with variable delays ⋮ Stability analysis of block boundary value methods for neutral pantograph equation

Uses Software

• RODAS

Cites Work

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• Stability of numerical methods for delay differential equations
• Strong contractivity properties of numerical methods for ordinary and delay differential equations
• Contractivity of Runge-Kutta methods with respect to forcing terms
• Stability analysis of Runge-Kutta methods for nonlinear delay differential equations
• Stability and error analysis of one-leg methods for nonlinear delay differential equations
• Asymptotic stability properties of \(\theta\)-methods for the pantograph equation
• Exact and discretized stability of the pantograph equation
• Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equations
• Nonlinear stability and D-convergence of Runge-Kutta methods for delay differential equations
• The discrete dynamics of nonlinear infinite-delay-differential equations
• Stability analysis of \(\theta\)-methods for neutral functional- differential equations
• On the \(\theta\)-method for delay differential equations with infinite lag
• Non-linear stability of a general class of differential equation methods
• On the dynamics of a discretized neutral equation
• Stability of the Discretized Pantograph Differential Equation

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