Solving non-differentiable Hammerstein integral equations via first-order divided differences

In this paper, the behavior of derivative-free techniques to approximate solutions of nonlinear Hammerstein-type integral equations in Banach space C ( [ α , β ] ) as alternatives against the well-known Newton’s method is examined. In particular, from the well-known Kurchatov method, we construct a...

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Published in:Numerical algorithms 2024-10, Vol.97 (2), p.567-594
Main Authors: Hernández-Verón, M. A., Magreñán, Á. A., Martínez, Eulalia, Villalba, Eva G.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Approximation
Banach spaces
Computer Science
Derivatives
Integral equations
Integrals
Iterative methods
Nonlinear equations
Numeric Computing
Numerical Analysis
Operators (mathematics)
Original Paper
Partial differential equations
Theory of Computation
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Magreñán, Á. A.
Martínez, Eulalia
Villalba, Eva G.
description In this paper, the behavior of derivative-free techniques to approximate solutions of nonlinear Hammerstein-type integral equations in Banach space C ( [ α , β ] ) as alternatives against the well-known Newton’s method is examined. In particular, from the well-known Kurchatov method, we construct a uniparametric family of derivative-free iterative schemes in order to achieve an approximation of a solution of a Hammerstein-type integral equation with a non-differentiable Nemyskii operator. We compare the uniparametric family built and the Kurchatov method, obtaining improvements in the precision and also in the accessibility through studying its dynamic behavior.
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subjects Algebra
Algorithms
Approximation
Banach spaces
Computer Science
Derivatives
Integral equations
Integrals
Iterative methods
Nonlinear equations
Numeric Computing
Numerical Analysis
Operators (mathematics)
Original Paper
Partial differential equations
Theory of Computation
title Solving non-differentiable Hammerstein integral equations via first-order divided differences
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