IIT Jodhpur
Congratulations to Dr. Moumita Mandal for the acceptance of her research article in the journal International Journal of Nonlinear Analysis and Applications

Title: Projection and multi-projection methods for second kind Volterra-Hammerstein
integral equation
Authors: M. Mandal, K. Kant and G. Nelakanti
Journal: International Journal of Nonlinear Analysis and Applications
Volume: In Press
Year: 2020
Publisher: Semnan University

Abstract: In this article, we discuss the piecewise polynomial based Galerkin method to
approximate the solutions of second kind Volterra-Hammerstein integral equations. We
discuss the convergence of the approximate solutions to the exact solutions and obtain the
orders of convergence O(h^r ) and O(h^{2r} ), respectively, for Galerkin and its iterated Galerkin
methods in uniform norm, where h, r denote the norm of the partition and smoothness of
the kernel, respectively. We also obtain the superconvergence results for multi-Galerkin
and iterated multi-Galerkin methods. We show that iterated multi-Galerkin method has the
order of convergence O(h 3r ) in the uniform norm. Numerical results are provided to
demonstrate the theoretical results.