Article
Kyungpook Mathematical Journal 2020; 60(4): 869-881
Published online December 31, 2020
Copyright © Kyungpook Mathematical Journal.
A Regularization-direct Method to Numerically Solve First Kind Fredholm Integral Equation
Zahra Masouri*, Saeed Hatamzadeh
Department of Mathematics, Islamshahr Branch, Islamic Azad University (IAU), Tehran, Iran
e-mail : nmasouri@yahoo.com
Department of Electrical Engineering, Islamshahr Branch, Islamic Azad University (IAU), Tehran, Iran
e-mail : s.hatamzadeh@yahoo.com
Received: June 7, 2019; Revised: January 9, 2020; Accepted: May 30, 2020
Most first kind integral equations are ill-posed, and obtaining their numerical solution often requires solving a linear system of algebraic equations of large condition number, which may be difficult or impossible. This article proposes a regularization-direct method to numerically solve first kind Fredholm integral equations. The vector forms of block-pulse functions and related properties are applied to formulate the direct method and reduce the integral equation to a linear system of algebraic equations. We include a regularization scheme to overcome the ill-posedness of integral equation and obtain a stable numerical solution. Some test problems are solved using the proposed regularization-direct method to illustrate its efficiency for solving first kind Fredholm integral equations.
Keywords: first kind Fredholm integral equation, regularization method, block-pulse functions, vector forms, numerical solution