Superconvergent Nyström and Degenerate Kernel Methods for Integro-Differential Equations

Abdelmonaim Saou, Driss Sbibih, Mohamed Tahrichi and Domingo Barrera
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Abdelmonaim Saou: Team ANAA, ANO Laboratory, Faculty of Sciences, University Mohammed First, Oujda 60000, Morocco
Driss Sbibih: Team ANTO, ANO Laboratory, Faculty of Sciences, University Mohammed First, Oujda 60000, Morocco
Mohamed Tahrichi: Team ANAA, ANO Laboratory, Faculty of Sciences, University Mohammed First, Oujda 60000, Morocco
Domingo Barrera: Department of Applied Mathematics, University of Granada, Campus de Fuentenueva s/n, 18071 Granada, Spain

Mathematics, 2022, vol. 10, issue 6, 1-15

Abstract: The aim of this paper is to carry out an improved analysis of the convergence of the Nyström 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 2 r for degenerate kernel and Nyström methods, while, for the superconvergent and the iterated versions of theses methods, the obtained convergence orders are 3 r + 1 and 4 r , respectively. Moreover, we show that the optimal convergence order 4 r is restored at the partition knots for the approximate solutions. The obtained theoretical results are illustrated by some numerical examples.

Keywords: degenerate kernel method; Nyström method; Fredholm integro-differential equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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