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An h – p version of the Chebyshev spectral collocation method for nonlinear delay differential equations
Author(s) -
Meng Tingting,
Wang Zhongqing,
Yi Lijun
Publication year - 2019
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22318
Subject(s) - mathematics , chebyshev polynomials , chebyshev filter , chebyshev nodes , gauss , collocation (remote sensing) , nonlinear system , a priori and a posteriori , spectral method , collocation method , polynomial , norm (philosophy) , mathematical analysis , differential equation , computer science , ordinary differential equation , philosophy , physics , epistemology , quantum mechanics , machine learning , political science , law
We develop and analyze a spectral collocation method based on the Chebyshev–Gauss–Lobatto points for nonlinear delay differential equations with vanishing delays. We derive an a priori error estimate in the H 1 ‐norm that is completely explicit with respect to the local time steps and the local polynomial degrees. Several numerical examples are provided to illustrate the theoretical results.