Improved Iterative Solution of Linear Fredholm Integral Equations of Second Kind via Inverse-Free Iterative Schemes

José Manuel Gutiérrez, Miguel Ángel Hernández-Verón and Eulalia Martínez
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José Manuel Gutiérrez: Department of Mathematics and Computation, University of La Rioja, 26006 Logroño, Spain
Miguel Ángel Hernández-Verón: Department of Mathematics and Computation, University of La Rioja, 26006 Logroño, Spain
Eulalia Martínez: Instituto Universitario de Matemática Multidisciplinar, Universitat Politècnica de València, 46022 València, Spain

Mathematics, 2020, vol. 8, issue 10, 1-13

Abstract: This work is devoted to Fredholm integral equations of second kind with non-separable kernels. Our strategy is to approximate the non-separable kernel by using an adequate Taylor’s development. Then, we adapt an already known technique used for separable kernels to our case. First, we study the local convergence of the proposed iterative scheme, so we obtain a ball of starting points around the solution. Then, we complete the theoretical study with the semilocal convergence analysis, that allow us to obtain the domain of existence for the solution in terms of the starting point. In this case, the existence of a solution is deduced. Finally, we illustrate this study with some numerical experiments.

Keywords: Fredholm integral equation; iterative processes; Newton’s method; separable and non-separable kernels; local and semilocal convergence (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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