Superconvergent Nyström and Degenerate Kernel Methods for Integro-Differential Equations

Mathematics

Domingo Barrera¹  Abdelmonaim Saou²  Mohamed Tahrichi²  Driss Sbibih³ 

[1] Department of Applied Mathematics, University of Granada, Campus de Fuentenueva s/n, 18071 Granada, Spain;Team ANAA, ANO Laboratory, Faculty of Sciences, University Mohammed First, Oujda 60000, Morocco;Team ANTO, ANO Laboratory, Faculty of Sciences, University Mohammed First, Oujda 60000, Morocco;

关键词: degenerate kernel method;    Nyström method;    Fredholm integro-differential equation;   

DOI  :  10.3390/math10060893

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown