Superconvergence results of Legendre spectral projection methods for Volterra integral equations of second kind

Approximation methods for system of nonlinear Fredholm–Hammerstein integral equations

“…In Assari (2019a), Assari and Asadi-Mehregan (2019), Assari and Dehghan (2018), Assari et al discussed meshless Galerkin and meshless collocation methods for solving the single Fredholm-Hammerstein integral equation, whereas in Assari (2019b), P. Assari used a combination of collocation method with radial basis functions constructed on scattered points as a basis to find the numerical solution of single Fredholm-Hammerstein integral equation. In Chen et al (2007), Kant and Nelakanti (2020b), Kant and Nelakanti (2020a), , Long et al (2009), Mandal and Nelakanti (2018), Nahid and Nelakanti (2019) multi-projection (multi-collocation and multi-Galerkin) methods are proposed for solving single Fredholm integral equation and obtained superconvergence rates. In Mandal and Nelakanti (2019a), Mandal et al applied the multi-Galerkin and iterated multi-Galerkin methods for solving single weakly singular Fredholm-Hammerstein integral equation and obtained the improved superconvergence rates for iterated multi-Galerkin method.…”

On the numerical solution of Volterra integral equations on equispaced nodes

“…In light of such applications, a variety of numerical methods [4,5,9,13,17,21,31,32,33,34] have been developed to approximate the solution f in suitable spaces both in the case when the kernel is sufficiently smooth and when it is weakly singular. In order for treating the case of functions presenting algebraic singularities at the endpoints of the interval [0, 1] and/or on the boundary of D, weighted global approximation methods have been recently introduced and studied in [10,14].…”