NDLI: Superconvergent Nyström and Degenerate Kernel Methods for Integro-Differential Equations

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Superconvergent Nyström and Degenerate Kernel Methods for Integro-Differential Equations

Content Provider	MDPI
Author	Saou, Abdelmonaim Sbibih, Driss Tahrichi, Mohamed Barrera, Domingo
Copyright Year	2022
Description	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 $2r$ for degenerate kernel and Nyström 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.
Starting Page	893
e-ISSN	22277390
DOI	10.3390/math10060893
Journal	Mathematics
Issue Number	6
Volume Number	10
Language	English
Publisher	MDPI
Publisher Date	2022-03-11
Access Restriction	Open
Subject Keyword	Mathematics Mathematical Physics Degenerate Kernel Method Nyström Method Fredholm Integro-differential Equation
Content Type	Text
Resource Type	Article

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