A New Class of Fredholm Integral Equations of the Second Kind with Non Symmetric Kernel: Solving by Wavelets Method

被引：2

作者：

Mennouni, Abdelaziz ^{[1
]}

Ramdani, Nedjem Eddine ^{[1
]}

Zennir, Khaled ^{[2
,3
]}

机构：

[1] Univ Mostefa Ben Boulaid Batna 2, Dept Math, Fesdis, Batna, Algeria

[2] Qassim Univ, Coll Sci & Arts, Dept Math, Buraydah, Saudi Arabia

[3] Univ 20 Aout 1955 Skikda, Dept Math, Lab LAMAHIS, Skikda 21000, Algeria

来源：

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA | 2021年 / 39卷 / 06期

关键词：

Fredholm integral equation; Non symmetric kernel; Wavelet basis; Toeplitz matrix; Condition number; NUMERICAL-SOLUTION; 1ST KIND; GALERKIN METHODS; TRANSFORMS; BASES;

D O I：

10.5269/bspm.41734

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we introduce an efficient modification of the wavelets method to solve a new class of Fredholm integral equations of the second kind with non symmetric kernel. This method based on orthonormal wavelet basis, as a consequence three systems are obtained, a Toeplitz system and two systems with condition number close to 1. Since the preconditioned conjugate gradient normal equation residual (CGNR) and preconditioned conjugate gradient normal equation error (CGNE) methods are applicable, we can solve the systems in O(2n log(n)) operations, by using the fast wavelet transform and the fast Fourier transform.

引用

页码：67 / 80

页数：14

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