Hernández-Verón, M. A.; Yadav, Sonia; Martínez, Eulalia; Singh, Sukhjit Solving nonlinear integral equations with non-separable kernel via a high-order iterative process. (English) Zbl 1497.45006 Appl. Math. Comput. 409, Article ID 126385, 12 p. (2021). Summary: In this work we focus on location and approximation of a solution of nonlinear integral equations of Hammerstein-type when the kernel is non-separable through a high order iterative process. For this purpose, we approximate the non-separable kernel by means of a separable kernel and then, we perform a complete study about the convergence criteria for the approximated solution obtained to the solution of our first problem. Different examples have been tested in order to apply our theoretical results. Cited in 2 Documents MSC: 45G10 Other nonlinear integral equations 47H99 Nonlinear operators and their properties 65J15 Numerical solutions to equations with nonlinear operators Keywords:Newton’s iterative method; semilocal convergence study; Newton-Kantorovich conditions; majorizing sequences; error bounds; order of convergence; nonlinear integral equation PDFBibTeX XMLCite \textit{M. A. Hernández-Verón} et al., Appl. Math. Comput. 409, Article ID 126385, 12 p. (2021; Zbl 1497.45006) Full Text: DOI References: [1] Chandru, M.; Das, P.; Ramos, H., Numerical treatment of two-parameter singularly perturbed parabolic convection diffusion problems with non-smooth data, Math. Methods Appl. Sci., 41, 14, 5359-5387 (2018) · Zbl 1403.35024 [2] Cordero, A.; Hernández, M. A.; Romero, N.; Torregrosa, J. R., Semilocal convergence by using recurrence relations for a fifth-order method in banach spaces, J. Comput. Appl. 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