$ hp $-version collocation method for a class of nonlinear Volterra integral equations of the first kind
Numerical Analysis
2019-10-15 v2 Numerical Analysis
Abstract
In this paper, we present a collocation method for nonlinear Volterra integral equation of the first kind. This method benefits from the idea of -version projection methods. We provide an approximation based on the Legendre polynomial interpolation. The convergence of the proposed method is completely studied and an error estimate under the -norm is provided. Finally, several numerical experiments are presented in order to verify the obtained theoretical results.
Keywords
Cite
@article{arxiv.1810.00730,
title = {$ hp $-version collocation method for a class of nonlinear Volterra integral equations of the first kind},
author = {Khadijeh Nedaiasl and Raziyeh Dehbozorgi and Khosrow Maleknejad},
journal= {arXiv preprint arXiv:1810.00730},
year = {2019}
}
Comments
29 pages