Title: Discrete Legendre Spectral Methods for Hammerstein type Weakly Singular Nonlinear Fredholm Integral Equations.

Authors: Moumita Mandal, Kapil Kant, Gnaneshwar Nelakanti Journal: International Journal of Computer Mathematics Volume: In Press

Year: 2021

Publisher: Taylor & Francis

Abstract: In this article, we study the discrete version of Legendre spectral and iterated Legendre spectral techniques to solve the second kind Hammerstein type weakly singular integral equations. To obtain the convergence analysis, we use appropriate numerical quadrature rule and obtain the order O(n-r+1) discrete Legendre spectral method. If the quadrature rule is minimal then optimal rate is obtained O(n-r ) in iterated form of discrete Legendre spectral collocation method in and uniform norms. Numerical aspects are given to verify the hypothetical results.