Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

The hp discontinuous galerkin method for delay differential equations with nonlinear vanishing delay

Language

English

Abstract

We present the hp-version of the discontinuous Galerkin method for the numerical solution of delay differential equations with nonlinear vanishing delays and derive error bounds that are explicit in the time steps, the degrees of the approximating polynomials, and the regularity properties of the exact solutions. It is shown that the hp discontinuous Galerkin method exhibits exponential rates of convergence for smooth solutions on uniform meshes, and for nonsmooth solutions on geometrically graded meshes. The theoretical results are illustrated by various numerical examples. © 2013 Society for Industrial and Applied Mathematics.

Keywords

Discontinuous Galerkin method, Hp-version, Nonlinear vanishing delay, Pantograph delay differential equations, Spectral and exponential accuracy

Publication Date

2013

Source Publication Title

SIAM Journal on Scientific Computing

Volume

35

Issue

3

Start Page

A1604

End Page

A1620

Publisher

Society for Industrial and Applied Mathematics

DOI

10.1137/120901416

Link to Publisher's Edition

http://dx.doi.org/10.1137/120901416

ISSN (print)

10648275

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