@article{Amin2023, 
author = {A. Z. Amin and M. A. Abdelkawy and Amr Kamel Amin and António M. Lopes and Abdulrahim A. Alluhaybi and I. Hashim},
title = {Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {9},
pages = {20871-20891},
keywords = {system of mixed Volterra-Fredholm integral equations, spectral collocation method, shifted Legendre polynomials, shifted Legendre-Gauss-Lobatto quadrature},
url = {https://www.sciopen.com/article/10.3934/math.20231063},
doi = {10.3934/math.20231063},
abstract = {Integral equations play a crucial role in many scientific and engineering problems, though solving them is often challenging. This paper addresses the solution of multi-dimensional systems of mixed Volterra-Fredholm integral equations (SMVF-IEs) by means of a Legendre-Gauss-Lobatto collocation method. The one-dimensional case is addressed first. Afterwards, the method is extended to two-dimensional linear and nonlinear SMVF-IEs. Several numerical examples reveal the effectiveness of the approach and show its superiority in comparison to other alternative techniques for treating SMVF-IEs.}
}