An h-p Version of the Continuous Petrov-Galerkin Method for Nonlinear Delay Differential Equations

被引:14
作者
Meng, Tingting [1 ]
Yi, Lijun [1 ]
机构
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
基金
上海市自然科学基金; 中国国家自然科学基金;
关键词
Nonlinear delay differential equations; h-p version; Continuous Petrov-Galerkin method; Error analysis; FINITE-ELEMENT-METHOD; SPECTRAL COLLOCATION METHOD; PRIORI ERROR ANALYSIS; LEGENDRE; SUPERCONVERGENCE; STABILITY;
D O I
10.1007/s10915-017-0482-z
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We investigate an h-p version of the continuous Petrov-Galerkin time stepping method for nonlinear delay differential equations with vanishing delays. We derive a priori error estimates in the -, - and -norm that are completely explicit with respect to the local time steps, the local polynomial degrees, and the local regularity of the exact solution. Moreover, we show that the h-p version continuous Petrov-Galerkin scheme based on geometrically refined time steps and on linearly increasing approximation orders achieves exponential rates of convergence for solutions with start-up singularities. The theoretical results are illustrated by some numerical experiments.
引用
收藏
页码:1091 / 1114
页数:24
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