A mixed collocation scheme for solving second kind fredholm integral equations in [-1; 1]

被引：0
作者：
OCCORSIO D. [1 ,2 ]
RUSSO M.G. [1 ,2 ]
机构：
[1] Department of Mathematics Computer Science and Economics, University of Basilicata, Via dell'Ateneo Lucano 10, Potenza
[2] Istituto per le Applicazioni del Calcolo "Mauro Picone", Naples branch, National Research Council (C.N.R.) of Italy, Via P. Castellino 111, Napoli
来源：
Electronic Transactions on Numerical Analysis | 2021年 / 54卷
关键词：
Collocation method; Fredholm integral equations; Modified moments; Orthogonal polynomials; Polynomial approximation;
D O I：
10.1553/ETNA_VOL54S443
中图分类号：
O24 [计算数学];
学科分类号：
070102 ;
摘要：
In this paper we propose a suitable combination of two collocation methods based on the zeros of Jacobi polynomials in order to approximate the solution of Fredholm integral equations on [-1; 1]. One of the main interesting aspects of this procedure is that our approach is cheaper than the usual collocation method based on standard Lagrange interpolation using Jacobi zeros. Moreover, we can successfully manage functions with algebraic singularities at the endpoints. The error of the method is comparable with the error of the best polynomial approximation in suitable spaces of functions, equipped with the weighted uniform norm. The convergence and the stability of the method is proved, and some numerical tests, which confirm the theoretical estimates, are provided. © 2021, Kent State University.
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页码：443 / 459
页数：16
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