$B$-Convergence Theory of Runge--Kutta Methods for Stiff Volterra Functional Differential Equations with Infinite Integration Interval

DOI10.1137/130944837zbMath1330.65110OpenAlexW2173131798MaRDI QIDQ3453961

Yunfei Li, Shou-fu Li

Publication date: 2 December 2015

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/130944837

zbMATH Keywords

Runge-Kutta methodsVolterra functional differential equationslong time stiff computation\(B\)-convergence theory

Mathematics Subject Classification ID

Linear functional-differential equations (34K06) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for functional-differential equations (65L03) Numerical methods for functional equations (65Q20)

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Stability analysis of discontinuous Galerkin method for stiff Volterra functional differential equations ⋮ Stage-based interpolation Runge-Kutta methods for nonlinear Volterra functional differential equations ⋮ Dissipativity of variable-stepsize Runge-Kutta methods for nonlinear functional differential equations with application to Nicholson's blowflies models ⋮ An efficient IMEX method for nonlinear functional differential equations with state-dependent delay ⋮ Numerical Analysis and Computational Solution of Integro-Differential Equations ⋮ Unnamed Item ⋮ A Posteriori Error Analysis for Crank--Nicolson--Galerkin Type Methods for Reaction-Diffusion Equations with Delay ⋮ Dissipativity and Contractivity Analysis for Fractional Functional Differential Equations and their Numerical Approximations ⋮ A posteriori error estimates for fully discrete finite element method for generalized diffusion equation with delay ⋮ Delay-dependent elliptic reconstruction and optimal 𝐿^{∞}(𝐿²) a posteriori error estimates for fully discrete delay parabolic problems

Cites Work

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• \(B\)-theory of Runge-Kutta methods for stiff Volterra functional differential equations
• Classical theory of Runge-Kutta methods for Volterra functional differential equations
• High Order Contractive Runge–Kutta Methods for Volterra Functional Differential Equations
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• Numerical Methods for Delay Differential Equations

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