@Article{AAMM-12-2,
author = {Xiulian, Shi and Yanping, Chen and Yunqing, Huang and Huang, Fenglin},
title = {Spectral Collocation Methods for Second-Order Volterra Integro-Differential Equations with Weakly Singular Kernels},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2020},
volume = {12},
number = {2},
pages = {480--502},
abstract = {<p style="text-align: justify;">In this paper, a Jacobi spectral collocation approximation is proposed for the solution of second-order Volterra integro-differential equations with weakly singular kernels. The solution of such equations usually exhibits a singular behaviour at the origin. By using some suitable variable transformations, we obtain a new equation which is still weakly singular, but whose solution is as smooth as we like. Then the resulting equation is solved by standard spectral methods. We establish a rigorous error analysis for the proposed method, which shows that the numerical errors decay exponentially in $L^\infty$-norm and weighted $L^2$-norm. Finally, to perform the numerical simulation, a test example is considered with non-smooth solutions.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2019-0056},
url = {https://global-sci.com/article/73042/spectral-collocation-methods-for-second-order-volterra-integro-differential-equations-with-weakly-singular-kernels}
}