@Article{NMTMA-12-969, author = {}, 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} }