Legendre spectral collocation method for solving nonlinear fractional Fredholm integro-differential equations with convergence analysis - Tedjani, A. H.; Amin, A. Z.; Abdel-Aty, Abdel-Haleem; Abdelkawy, M. A.; Mahmoud, Mona (AIMS mathematics, 2024)
The main purpose of this work was to develop a spectrally accurate collocation method for solving nonlinear fractional Fredholm integro-differential equations (non-FFIDEs). A proposed spectral collocation method is based on the Legendre-Gauss-Lobatto collocation (L-G-LC) method in which the main idea is to use Caputo derivatives and Legendre-Gauss interpolation for nonlinear FFIDEs. A rigorous convergence analysis is provided and confirmed by numerical tests. In addition, we provide some numerical test cases to demonstrate that the approach can preserve the non-smooth solution of the underlying problem.