An $hp$-Version Chebyshev Spectral Collocation Method for Nonlinear Volterra Integro-Differential Equations with Weakly Singular Kernels
Year: 2019
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2018-0104
Numerical Mathematics: Theory, Methods and Applications, Vol. 12 (2019), Iss. 3 : pp. 969–994
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 26
Keywords: Chebyshev spectral collocation method nonlinear Volterra integro-differential equations weakly singular kernels error analysis.