On the attainable order of collocation methods for delay differential equations with proportional delay

DOI10.1023/A:1022351309662zbMath0965.65101OpenAlexW75478609MaRDI QIDQ1577727

Norio Takama, Yoshiaki Muroya, Emiko Ishiwata

Publication date: 14 August 2001

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1022351309662

zbMATH Keywords

collocation methodsdelay differential equationsoptimal orderproportional delaypantograph differential equationpantograph integral equation

Mathematics Subject Classification ID

Related Items (21)

On the attainable order of collocation methods for pantograph integro-differential equations ⋮ Continuous Galerkin methods on quasi-geometric meshes for delay differential equations of pantograph type ⋮ Multilevel correction for collocation solutions of Volterra integral equations with proportional delays ⋮ Ana priorierror analysis of thehp-version of theC⁰-continuous Petrov-Galerkin method for nonlinear second-order delay differential equations ⋮ Rational approximation method for delay differential equations with proportional delay ⋮ Optimal superconvergence results for Volterra functional integral equations with proportional vanishing delays ⋮ A super-attainable order in collocation methods for differential equations with proportional delay ⋮ Analytic solutions to a class of nonlinear infinite-delay-differential equations ⋮ Collocation methods for Volterra functional integral equations with non-vanishing delays ⋮ An \(h\)-\(p\) version of the continuous Petrov-Galerkin method for nonlinear delay differential equations ⋮ Extended two-dimensional DTM and its application on nonlinear PDEs with proportional delay ⋮ Superconvergence of discontinuous Galerkin methods for nonlinear delay differential equations with vanishing delay ⋮ Asymptotical stability of numerical methods with constant stepsize for pantograph equations ⋮ Superconvergence in collocation methods on quasi-graded meshes for functional differential equations with vanishing delays ⋮ An \(hp\)-version of the discontinuous Galerkin time-stepping method for nonlinear second-order delay differential equations with vanishing delays ⋮ Superconvergence in collocation methods for Volterra integral equations with vanishing delays ⋮ Analytic solution of multipantograph equation ⋮ Recent advances in the numerical analysis of Volterra functional differential equations with variable delays ⋮ Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays ⋮ On collocation methods for delay differential and Volterra integral equations with proportional delay ⋮ An \(h\)-\(p\) version of the continuous Petrov-Galerkin time stepping method for nonlinear second-order delay differential equations

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