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 the appropriate numerical quadrature rule and obtain the order in discrete Legendre spectral method. If the quadrature rule is minimal, i.e. the number of quadrature nodes and the dimension of the approximating subspace are same, then the optimal rate is obtained in iterated form of discrete Legendre spectral collocation method in norm and uniform norm. Numerical aspects are given to verify the hypothetical results.
Acknowledgments
The research work of Gnaneshwar Nelakanti was supported by the National Board for Higher Mathematics, India, research project: No02011/6/2019NBHM(R.P)/R & D II /1236 dated 28/1/2019.
Disclosure statement
No potential conflict of interest was reported by the author(s).