NDLI: Combining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind

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Combining Nyström Methods for a Fast Solution of Fredholm Integral Equations of the Second Kind

Content Provider	MDPI
Author	Mezzanotte, Domenico Occorsio, Donatella Russo, Maria Grazia
Copyright Year	2021
Description	In this paper, we propose a suitable combination of two different Nyström methods, both using the zeros of the same sequence of Jacobi polynomials, in order to approximate the solution of Fredholm integral equations on $[-1,1]$ . The proposed procedure is cheaper than the Nyström scheme based on using only one of the described methods . Moreover, we can successfully manage functions with possible algebraic singularities at the endpoints and kernels with different pathologies. The error of the method is comparable with that of the best polynomial approximation in suitable spaces of functions, equipped with the weighted uniform norm. The convergence and the stability of the method are proved, and some numerical tests that confirm the theoretical estimates are given.
Starting Page	2652
e-ISSN	22277390
DOI	10.3390/math9212652
Journal	Mathematics
Issue Number	21
Volume Number	9
Language	English
Publisher	MDPI
Publisher Date	2021-10-20
Access Restriction	Open
Subject Keyword	Mathematics Industrial Engineering Fredholm Integral Equations Nyström Methods Product Integration Rules Orthogonal Polynomials
Content Type	Text
Resource Type	Article

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