A mixed collocation scheme for solving second kind Fredholm integral equations in [-1,1]

Electronic Transactions on Numerical Analysis

article

Donatella Occorsio¹  Maria Grazia Russo¹ 

[1] Department of Mathematics, Computer Science and Economics, University of Basilicata;Istituto per le Applicazioni del Calcolo “Mauro Picone”, Naples branch, National Research Council

关键词: Fredholm integral equations;    collocation method;    polynomial approximation;    orthogonal polynomials;    modified moments;   

DOI  :  10.1553/etna_vol54s443

学科分类：数学（综合）

来源: Kent State University * Institute of Computational Mathematics

【 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.

【 授权许可】

Unknown