Legendre spectral projection methods for Fredholm integral equations of first kind-Reference-Cited by-同舟云学术

Legendre spectral projection methods for Fredholm integral equations of first kind

Published:2022-07-23 Issue:0 Volume:0 Page:
ISSN:0928-0219
Container-title:Journal of Inverse and Ill-posed Problems
language:en
Short-container-title:

Author:

Patel Subhashree¹^ORCID,Panigrahi Bijaya Laxmi²^ORCID,Nelakanti Gnaneshwar³

Affiliation:

1. Department of Mathematics , Sambalpur University , Odisha - 768019 , India

2. Department of Mathematics , Gangadhar Meher University , Odisha - 768004 , India

3. Department of Mathematics , Indian Institute of Technology , Kharagpur - 721302 , India

Abstract

Abstract In this paper, we discuss the Legendre spectral projection method for solving Fredholm integral equations of the first kind using Tikhonov regularization. First, we discuss the convergence analysis under an a priori parameter strategy for the Tikhonov regularization using Legendre polynomial basis functions, and we obtain the optimal convergence rates in the uniform norm. Next, we discuss Arcangeli’s discrepancy principle to find a suitable regularization parameter and obtain the optimal order of convergence in uniform norm. We present numerical examples to illustrate the theoretical results.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/jiip-2020-0104/pdf

Reference23 articles.

1. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic, Dordrecht, 1994.

2. C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, Spectral Methods: Fundamentals in Single Domains, Springer, Berlin, 2006.

3. Z. Chen, S. Cheng, G. Nelakanti and H. Yang, A fast multiscale Galerkin method for the first kind ill-posed integral equations via Tikhonov regularization, Int. J. Comput. Math. 87 (2010), no. 3, 565–582.

4. Z. Chen, Y. Xu and H. Yang, Fast collocation methods for solving ill-posed integral equations of the first kind, Inverse Problems 24 (2008), no. 6, Article ID 065007.

5. H. W. Engl and C. W. Groetsch, Projection-regularization methods for linear operator equations of the first kind, Special Program on Inverse Problems, Proc. Centre Math. Anal. Austral. Nat. Univ. 17, Austrailian National University, Canberra (1988), 17–31.

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On the numerical solution of weakly singular integral equations of the first kind using a regularized projection method;International Journal of Computer Mathematics;2024-05-03

2. Discrete Legendre spectral projection-based methods for Tikhonov regularization of first kind Fredholm integral equations;Applied Numerical Mathematics;2024-04

3. Jacobi spectral projection methods for Fredholm integral equations of the first kind;Numerical Algorithms;2023-08-22

4. Multi-projection methods for Fredholm integral equations of the first kind;International Journal of Computer Mathematics;2022-11-29

5. Legendre spectral multi-projection methods for Fredholm integral equations of the first kind;Advances in Operator Theory;2022-08-30