The hp discontinuous Galerkin method for delay differential equations with nonlinear vanishing delay
Huang, Qiumei and Xie, Hehu and Brunner, Hermann (2013) The hp discontinuous Galerkin method for delay differential equations with nonlinear vanishing delay. SIAM Journal on Scientific Computing, 35 (3). A1604-A1620. ISSN 1064-8275 (https://doi.org/10.1137/120901416)
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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.
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Item type: Article ID code: 46555 Dates: DateEvent2013PublishedSubjects: Science > Mathematics Department: Faculty of Science > Mathematics and Statistics Depositing user: Pure Administrator Date deposited: 23 Jan 2014 12:57 Last modified: 15 Sep 2024 04:29 URI: https://strathprints.strath.ac.uk/id/eprint/46555