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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Bibliographic Details
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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Summary: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.
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-023-01715-6