International Journal of Nonlinear Analysis and Applications

Projection and multi-projection methods for second kind Volterra-Hammerstein integral equation

Document Type : Research Paper

Authors

1 Assistant Professor, Department of Mathematics, Indian Institute of Technology Jodhpur, Rajasthan-342037, India.

2 Department of Mathematics Indian Institute of Technology Kharagpur, Kharagpur - 721 302, India

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(hr) and O(h2r), respectively, for Galerkin and its iterated Galerkin methods in uniform norm, where h, r denotes 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(h3r) in the uniform norm. Numerical results are provided to demonstrate the theoretical results.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 2
November 2021
Pages 275-291
  • Receive Date: 08 September 2019
  • Accept Date: 13 April 2020