A Picard-Type Iterative Scheme for Fredholm Integral Equations of the Second Kind

José M. Gutiérrez and Miguel Á. Hernández-Verón
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José M. Gutiérrez: Department of Mathematics and Computer Sciences, University of La Rioja, 26006 Logroño, Spain
Miguel Á. Hernández-Verón: Department of Mathematics and Computer Sciences, University of La Rioja, 26006 Logroño, Spain

Mathematics, 2021, vol. 9, issue 1, 1-15

Abstract: In this work, we present an application of Newton’s method for solving nonlinear equations in Banach spaces to a particular problem: the approximation of the inverse operators that appear in the solution of Fredholm integral equations. Therefore, we construct an iterative method with quadratic convergence that does not use either derivatives or inverse operators. Consequently, this new procedure is especially useful for solving non-homogeneous Fredholm integral equations of the first kind. We combine this method with a technique to find the solution of Fredholm integral equations with separable kernels to obtain a procedure that allows us to approach the solution when the kernel is non-separable.

Keywords: Fredholm integral equation; Newton’s method; iterative processes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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