Legendre multi-Galerkin methods for Fredholm integral equations with weakly singular kernel and the corresponding eigenvalue problem

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:346

Article

Panigrahi, Bijaya Laxmi¹  Mandal, Moumita²  Nelakanti, Gnaneshwar³ 

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

[2] VIT Univ, Dept Math, Vellore 632014, Tamil Nadu, India

[3] Indian Inst Technol, Dept Math, Kharagpur 721302, W Bengal, India

关键词: Legendre spectral methods;    Multi-Galerkin methods;    Fredholm integral equations;    Eigenvalue problem;    Weakly singular kernel;   

DOI  :  10.1016/j.cam.2018.07.010

来源: Elsevier

【 摘 要 】

In this paper, we consider Legendre multi-Galerkin methods to solve Fredholm integral equations of the second kind with weakly singular kernel and the corresponding eigenvalue problem. We obtain the convergence rates for the approximated solution and iterated solution in weakly singular Fredholm integral equations of the second kind in both L-2 and infinity-norm. We also establish error bounds of approximated eigenelements with exact eigenelements in the eigenvalue problem of a compact integral operator with weakly singular kernel in both infinity and L-2-norm. Numerical examples are presented to prove the theoretical estimates. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free