Jacobi spectral projectionmethods for Fredholm integral equations of the first kind

被引：1

作者：

Patel, Subhashree ^{[1
]}

Panigrahi, Bijaya Laxmi ^{[2
]}

机构：

[1] Sambalpur Univ, Dept Math, Sambalpur 768019, Odisha, India

[2] Gangadhar Meher Univ, Dept Math, Sambalpur 768004, Odisha, India

来源：

NUMERICAL ALGORITHMS | 2024年 / 96卷 / 01期

关键词：

Ill-posed problems; Fredholm integral equation of the first kind; Galerkin method; Tikhonov regularization method; Jacobi polynomials; REGULARIZED APPROXIMATION; CONVERGENCE ANALYSIS;

D O I：

10.1007/s11075-023-01638-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we employ Tikhonov regularization method with the projection methods using Jacobi polynomial bases to the first kind of Fredholm integral equations to find the approximate solution. We discuss the convergence analysis and obtain the convergence rates in L-omega alpha,beta(2) norm under a priori parameter choice strategy. We also consider the Engl-type discrepancy principle as a posteriori parameter strategy for finding the regularization parameter and also evaluate the convergence rate which is of optimal order. Finally, we provide the numerical experiments to justify the theoretical results.

引用

页码：33 / 57

页数：25

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