Nonlinear stability of general linear methods for neutral delay differential equations

DOI10.1016/J.CAM.2008.05.050zbMath1167.65046OpenAlexW2041676064MaRDI QIDQ1002199

Wan-Sheng Wang, Kai Su, Shou-fu Li

Publication date: 25 February 2009

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

Full work available at URL: https://doi.org/10.1016/j.cam.2008.05.050

zbMATH Keywords

numerical experimentsnumerical stabilitybackward differentiation formulaegeneral linear methodsnonlinear neutral delay differential equationsalgebraic stabilitymulti-step Runge-Kutta methods

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Stochastic functional-differential equations (34K50) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Neutral functional-differential equations (34K40)

Related Items (14)

Asymptotic stability of solution to nonlinear neutral and Volterra functional differential equations in Banach spaces ⋮ Uniform ultimate boundedness of numerical solutions to nonlinear neutral delay differential equations ⋮ Stability of linear multistep methods for nonlinear neutral delay differential equations in Banach space ⋮ Numerical approximation to semi-linear stiff neutral equations via implicit-explicit general linear methods ⋮ The asymptotic behaviour of theθ-methods with constant stepsize for the generalized pantograph equation ⋮ Stepsize restrictions for nonlinear stability properties of neutral delay differential equations ⋮ A Posteriori Error Analysis for Crank--Nicolson--Galerkin Type Methods for Reaction-Diffusion Equations with Delay ⋮ On \(A\)-stable one-leg methods for solving nonlinear Volterra functional differential equations ⋮ Contractivity and exponential stability of solutions to nonlinear neutral functional differential equations in Banach spaces ⋮ On the one-leg methods for solving nonlinear neutral differential equations with variable delay ⋮ A posteriori error estimates for fully discrete finite element method for generalized diffusion equation with delay ⋮ Stability analysis of Runge-Kutta methods for nonlinear functional differential and functional equations ⋮ Delay-dependent elliptic reconstruction and optimal 𝐿^{∞}(𝐿²) a posteriori error estimates for fully discrete delay parabolic problems ⋮ A multi-domain Legendre spectral collocation method for nonlinear neutral equations with piecewise continuous argument

Cites Work

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• The asymptotic stability of one-parameter methods for neutral differential equations
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• NGP(\(\alpha\))-stability of general linear methods for NDDEs
• Numerical stability of nonlinear delay differential equations of neutral type
• Stability analysis of numerical methods for systems of neutral delay-differential equations
• Nonlinear stability of one-leg methods for delay differential equations of neutral type
• Nonlinear stability of Runge-Kutta methods for neutral delay differential equations
• Stability and $B$-convergence properties of multistep Runge-Kutta methods
• Linear stability of general linear methods for systems of neutral delay differential equations
• On error growth functions of Runge-Kutta methods

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