@Article{NMTMA-12-969,
author = {Hongli Jia, Yang Yang and Zhongqing Wang},
title = {An $hp$-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2019},
volume = {12},
number = {3},
pages = {969--994},
abstract = {
This paper presents an $hp$-version Chebyshev spectral collocation method for
nonlinear Volterra integro-differential equations with weakly singular kernels. The $hp$-version error bound of the collocation method under the $H$1-norm is established on an
arbitrary mesh. Numerical experiments demonstrate the effectiveness of the proposed
method.
},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.OA-2018-0104},
url = {http://global-sci.org/intro/article_detail/nmtma/13139.html}
}
TY - JOUR
T1 - An $hp$-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels
AU - Hongli Jia, Yang Yang & Zhongqing Wang
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 969
EP - 994
PY - 2019
DA - 2019/04
SN - 12
DO - http://doi.org/10.4208/nmtma.OA-2018-0104
UR - https://global-sci.org/intro/article_detail/nmtma/13139.html
KW - Chebyshev spectral collocation method, nonlinear Volterra integro-differential equations, weakly singular kernels, error analysis.
AB -
This paper presents an $hp$-version Chebyshev spectral collocation method for
nonlinear Volterra integro-differential equations with weakly singular kernels. The $hp$-version error bound of the collocation method under the $H$1-norm is established on an
arbitrary mesh. Numerical experiments demonstrate the effectiveness of the proposed
method.
Hongli Jia, Yang Yang and Zhongqing Wang. (2019). An $hp$-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels.
Numerical Mathematics: Theory, Methods and Applications. 12 (3).
969-994.
doi:10.4208/nmtma.OA-2018-0104
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