A new method for solving three-dimensional nonlinear Fredholm integral equations by Haar wavelet

被引：4

作者：

Kazemi, Manochehr ^{[1
]}

Torkashvand, Vali ^{[2
,3
]}

Ezzati, Reza ^{[4
]}

机构：

[1] Islamic Azad Univ, Ashtian Branch, Dept Math, Ashtian, Iran

[2] Farhangian Univ, Dept Math, Tehran, Iran

[3] Islamic Azad Univ, Shahr E Qods Branch, Young Researchers & Elite club, Tehran, Iran

[4] Islamic Azad Univ, Karaj Branch, Dept Math, Karaj, Iran

来源：

INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS | 2021年 / 12卷 / 02期

关键词：

Three-dimensional integral equations; Three-dimensional Haar wavelet; Lipschitz condition; Successive approximations; NUMERICAL-SOLUTION; QUADRATURE-RULES; EXISTENCE;

D O I：

10.22075/ijnaa.2020.20860.2207

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, a new iterative method of successive approximations based on Haar wavelets is proposed for solving three-dimensional nonlinear Fredholm integral equations. The convergence of the method is verified. The error estimation and numerical stability of the proposed method are provided in terms of Lipschitz condition. Conducting numerical experiments confirm the theoretical results of the proposed method and endorse the accuracy of the method.

引用

页码：115 / +

页数：19

共 28 条

[1]

Abdelkawy MA, 2017, P ROMANIAN ACAD A, V18, P199

[2] On a method for solving a two-dimensional nonlinear integral equation of the second kind [J].

Abdou, M. A. ;

Badr, A. A. ;

Soliman, M. B. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (12) :3589-3598

[3]

Agarwal R. P., 2012, ABST APPL ANAL, V2012

[4]

Almousa M., 2016, AIP C P, V020053

[5] Utilizing artificial neural network approach for solving two-dimensional integral equations [J].

Asady B. ;

Hakimzadegan F. ;

Nazarlue R. .

Mathematical Sciences, 2014, 8 (1)

[6] Using operational matrix of two-dimensional Bernstein polynomials for solving two-dimensional integral equations of fractional order [J].

Asgari, M. ;

Ezzati, R. .

APPLIED MATHEMATICS AND COMPUTATION, 2017, 307 :290-298

[7]

Atkinson K., 2011, The numerical solution of integral equations of sencond kind

[8] PROJECTION AND ITERATED PROJECTION METHODS FOR NONLINEAR INTEGRAL-EQUATIONS [J].

ATKINSON, KE ;

POTRA, FA .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1987, 24 (06) :1352-1373

[9] A new method based on Haar wavelet for the numerical solution of two-dimensional nonlinear integral equations [J].

Aziz, Imran ;

Siraj-ul-Islam ;

Khan, Fawad .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2014, 272 :70-80

[10] Quadrature rules for numerical integration based on Haar wavelets and hybrid functions [J].

Aziz, Imran ;

Siraj-ul-Islam ;

Khan, Wajid .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (09) :2770-2781

← 1 2 3 →