Department of Mathematics
Discontinuous Galerkin methods for delay differential equations of pantograph type
This paper is concerned with the application of the discontinuous Galerkin method to delay differential equations with vanishing delay qt (0 < q < 1). Our aim is to establish optimal global and local superconvergence results on uniform meshes and compare these with analogous estimates for collocation methods. The theoretical results are illustrated by a broad range of numerical examples. © 2010 Society for Industrial and Applied Mathematics.
Discontinuous Galerkin method, Optimal order of superconvergence, Pantograph delay differential equations, Vanishing proportional delay
Source Publication Title
SIAM Journal on Numerical Analysis
Society for Industrial and Applied Mathematics
Brunner, Hermann, Qiumei Huang, and Hehu Xie. "Discontinuous Galerkin methods for delay differential equations of pantograph type." SIAM Journal on Numerical Analysis 48.5 (2010): 1944-1967.