Continuous Galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type

DOI10.3934/dcds.2016039zbMath1351.65047OpenAlexW2482155261MaRDI QIDQ321535

Hermann Brunner, Qiumei Huang, Xiuxiu Xu

Publication date: 14 October 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2016039

zbMATH Keywords

numerical examplecontinuous Galerkin methodsuperconvergencenonlinear vanishing delaypantograph delay differential equationquasi-geometric mesh

Mathematics Subject Classification ID

Related Items (14)

Superconvergence of discontinuous Galerkin method for neutral delay differential equations ⋮ A new numerical method to solve pantograph delay differential equations with convergence analysis ⋮ Ana priorierror analysis of thehp-version of theC⁰-continuous Petrov-Galerkin method for nonlinear second-order delay differential equations ⋮ An efficient IMEX method for nonlinear functional differential equations with state-dependent delay ⋮ Superconvergent postprocessing of the continuous Galerkin time stepping method for nonlinear initial value problems with application to parabolic problems ⋮ An \(h\)-\(p\) version of the continuous Petrov-Galerkin method for Volterra delay-integro-differential equations ⋮ An \(h\)-\(p\) version of the continuous Petrov-Galerkin method for nonlinear delay differential equations ⋮ Discontinuous Galerkin Methods for Multi-Pantograph Delay Differential Equations ⋮ Superconvergence of discontinuous Galerkin methods for nonlinear delay differential equations with vanishing delay ⋮ Optimal convergence orders of fully geometric mesh one-leg methods for neutral differential equations with vanishing variable delay ⋮ The continuous Galerkin finite element methods for linear neutral delay differential equations ⋮ An \(hp\)-version of the discontinuous Galerkin time-stepping method for nonlinear second-order delay differential equations with vanishing delays ⋮ An \(h\)-\(p\) version of the continuous Petrov-Galerkin time stepping method for nonlinear second-order delay differential equations ⋮ On Discontinuous and Continuous Approximations to Second-Kind Volterra Integral Equations

Cites Work

• Unnamed Item
• Stability of collocation methods for delay differential equations with vanishing delays
• The Galerkin continuous finite element method for delay-differential equation with a variable term
• Asymptotic stability properties of \(\theta\)-methods for the pantograph equation
• On the attainable order of collocation methods for delay differential equations with proportional delay
• On the \(\theta\)-method for delay differential equations with infinite lag
• Stability of Runge-Kutta methods for the generalized pantograph equation
• Superconvergence in collocation methods on quasi-graded meshes for functional differential equations with vanishing delays
• Geometric meshes in collocation methods for Volterra integral equations with proportional delays
• Local Superconvergence of Continuous Galerkin Solutions for Delay Differential Equations of Pantograph Type
• Superconvergence of a Dg Method for First-Order Linear Delay Differential Equations
• Discontinuous Galerkin Methods for Delay Differential Equations of Pantograph Type
• Superconvergence of Discontinuous Galerkin Solutions for Delay Differential Equations of Pantograph Type
• Discontinuous Galerkin Methods for Ordinary Differential Equations
• On the generalized pantograph functional-differential equation
• Preservation of superconvergence in the numerical integration of delay differential equations with proportional delay
• Numerical Methods for Delay Differential Equations
• Collocation Methods for Volterra Integral and Related Functional Differential Equations

This page was built for publication: Continuous Galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type