Superconvergent Nyström and Degenerate Kernel Methods for Integro-Differential Equations Saou, Abdelmonaim Barrera Rosillo, Domingo Degenerate kernel method Nyström method Fredholm integro-differential equation This research received no external funding and APC was funded by University of Granada. The aim of this paper is to carry out an improved analysis of the convergence of the Nystrom and degenerate kernel methods and their superconvergent versions for the numerical solution of a class of linear Fredholm integro-differential equations of the second kind. By using an interpolatory projection at Gauss points onto the space of (discontinuous) piecewise polynomial functions of degree <= r - 1, we obtain convergence order 2r for degenerate kernel and Nystrom methods, while, for the superconvergent and the iterated versions of theses methods, the obtained convergence orders are 3r + 1 and 4r, respectively. Moreover, we show that the optimal convergence order 4r is restored at the partition knots for the approximate solutions. The obtained theoretical results are illustrated by some numerical examples. 2022-04-18T11:16:46Z 2022-04-18T11:16:46Z 2022-03-11 info:eu-repo/semantics/article Saou, A... [et al.]. Superconvergent Nyström and Degenerate Kernel Methods for Integro-Differential Equations. Mathematics 2022, 10, 893. [https://doi.org/10.3390/math10060893] http://hdl.handle.net/10481/74327 10.3390/math10060893 eng http://creativecommons.org/licenses/by/3.0/es/ info:eu-repo/semantics/openAccess Atribución 3.0 España MDPI