Department of Mathematics
The hp discontinuous galerkin method for delay differential equations with nonlinear vanishing delay
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.
Discontinuous Galerkin method, Hp-version, Nonlinear vanishing delay, Pantograph delay differential equations, Spectral and exponential accuracy
Source Publication Title
SIAM Journal on Scientific Computing
Society for Industrial and Applied Mathematics
Link to Publisher's Edition
Huang, Qiumei, Hehu Xie, and Hermann Brunner. "The hp discontinuous galerkin method for delay differential equations with nonlinear vanishing delay." SIAM Journal on Scientific Computing 35.3 (2013): A1604-A1620.