The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part I: Convergence Results

DOI10.1137/130935550zbMath1330.65122OpenAlexW2236801637MaRDI QIDQ3462234

Stefano Maset

Publication date: 5 January 2016

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

Full work available at URL: https://doi.org/10.1137/130935550

zbMATH Keywords

convergencecollocation methodfinite element methodboundary value problemsneutral functional differential equationspectal element method

Mathematics Subject Classification ID

Neutral functional-differential equations (34K40) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Boundary value problems for functional-differential equations (34K10) Numerical methods for functional-differential equations (65L03)

Related Items

15 Years or So of Pseudospectral Collocation Methods for Stability and Bifurcation of Delay Equations ⋮ The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part I: Convergence Results ⋮ The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part II: Differential Equations with Deviating Arguments ⋮ Piecewise orthogonal collocation for computing periodic solutions of renewal equations ⋮ Pseudospectral discretization of delay differential equations in sun-star formulation: results and conjectures ⋮ Collocation of next-generation operators for computing the basic reproduction number of structured populations ⋮ Convergence Analysis of Collocation Methods for Computing Periodic Solutions of Retarded Functional Differential Equations ⋮ Collocation Techniques for Structured Populations Modeled by Delay Equations ⋮ An abstract framework in the numerical solution of boundary value problems for neutral functional differential equations

Uses Software

• Matlab

Cites Work

• Unnamed Item
• Unnamed Item
• Finite element boundary value integration of Wheeler-Feynman electrodynamics
• Boundary value problems for systems of functional differential equations.
• Optimal order spline methods for nonlinear differential and integro-differential equations
• Stability of piecewise polynomial collocation for computing periodic solutions of delay differential equations
• The numerical solution of boundary value problems for second order functional differential equations by finite differences
• Convergence of a boundary value difference equation for computing periodic solutions of neutral delay differential equations
• Collocation schemes for periodic solutions of neutral delay differential equations
• The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part I: Convergence Results
• The Collocation Method in the Numerical Solution of Boundary Value Problems for Neutral Functional Differential Equations. Part II: Differential Equations with Deviating Arguments
• Collocation Methods for Integro-Differential Equations
• Interpolation correction for collocation solutions of Fredholm integro-differential equations
• Orthogonal collocation for a nonlinear integro-differential equation
• Spectral Methods in MATLAB
• Computation of Mixed Type Functional Differential Boundary Value Problems