Fourth-order iterations for solving Hammerstein integral equations

DOI10.1016/j.apnum.2008.05.005zbMath1169.65119OpenAlexW1993164738WikidataQ112880209 ScholiaQ112880209MaRDI QIDQ1015905

José Antonio Ezquerro, Miguel A. Hernández

Publication date: 30 April 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2008.05.005

zbMATH Keywords

Banach spacessemilocal convergenceNewton-Kantorovich methodnonlinear operator equationsmultipoint iterationsnonlinear Hammerstein integral equationGauss-Legendre quadrature formulas

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Numerical solutions to equations with nonlinear operators (65J15)

Related Items (7)

Semilocal convergence and its computational efficiency of a seventh-order method in Banach spaces ⋮ On a two-step optimal Steffensen-type method: relaxed local and semi-local convergence analysis and dynamical stability ⋮ Numerical solution of nonlinear Volterra-Fredholm-Hammerstein integral equations via collocation method based on radial basis functions ⋮ Study on convergence and error of a numerical method for solving systems of nonlinear Fredholm–Volterra integral equations of Hammerstein type ⋮ Optimal approximation to a class of nonlinear evolution equations ⋮ SEMI-ORTHOGONAL SPLINE SCALING FUNCTIONS FOR SOLVING HAMMERSTEIN INTEGRAL EQUATIONS ⋮ Semilocal convergence of a sixth-order method in Banach spaces

Cites Work

• The Newton-Kantorovich method under mild differentiability conditions and the Ptâk error estimates
• Halley's method for operators with unbounded second derivative
• A method for finding sharp error bounds for Newton's method under the Kantorovich assumptions
• The application of an inverse-free Jarratt-type approximation to nonlinear integral equations of Hammerstein-type
• An adaptive version of a fourth-order iterative method for quadratic equations
• Generalized differentiability conditions for Newton's method
• Numerical Solvability of Hammerstein Integral Equations of Mixed Type
• A variant of Newton's method with accelerated third-order convergence
• Chebyshev's approximation algorithms and applications
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