On the regularization method for Fredholm integral equations with odd weakly singular kernel

被引：0

作者：

Noureddine Benrabia

Hamza Guebbai

机构：

[1] Université Mohamed-Chérif Messaadia Souk Ahras,Département de Mathématiques

[2] Université 8 Mai 1945 Guelma,Département de Mathématiques

来源：

Computational and Applied Mathematics | 2018年 / 37卷

关键词：

Integral equations; Weak singularity; Convolution; Fourier series; 45B05; 45E99; 65R20; 65T40;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this paper, we propose a numerical method to approach the solution of a Fredholm integral equation with a weakly singular kernel by applying the convolution product as a regularization operator and the Fourier series as a projection. Preliminary numerical results show that the order of convergence of the method is better than the one of conventional projection methods.

引用

页码：5162 / 5174

页数：12

共 50 条

[1] On the regularization method for Fredholm integral equations with odd weakly singular kernel
Benrabia, Noureddine
Guebbai, Hamza
[J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (04): : 5162 - 5174
[2] Reproducing kernel method for a class of weakly singular Fredholm integral equations
Alvandi, Azizallah
Paripour, Mahmoud
[J]. JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, 2018, 12 (04): : 409 - 414
[3] Regularization and Fourier Series for Fredholm Integral Equations of the Second Kind with a Weakly Singular Kernel
Guebbai, Hamza
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2018, 39 (01) : 1 - 10
[4] The approximate solution of a class of Fredholm integral equations with a weakly singular kernel
Babolian, E.
Hajikandi, A. Arzhang
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (05) : 1148 - 1159
[5] A new Laguerre wavelets-based method for solving Fredholm integral equations with weakly singular logarithmic kernel
Behera, Srikanta
Ray, Santanu Saha
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2024,
[6] Numerical solutions for Fredholm integral equations of the second kind with weakly singular kernel using spectral collocation method
Yang, Yin
Tang, Zhuyan
Huang, Yunqing
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2019, 349 : 314 - 324
[7] Discrete Legendre Collocation Methods for Fredholm-Hammerstein Integral Equations with Weakly Singular Kernel
Panigrahi, Bijaya Laxmi
[J]. MATHEMATICS AND COMPUTING (ICMC 2018), 2018, 253 : 315 - 328
[8] Bernstein polynomials iterative method for weakly singular and fractional Fredholm integral equations
Bica, Alexandru Mihai
Satmari, Zoltan
[J]. STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2024, 69 (03): : 695 - 712
[9] Asymptotics on the Fredholm integral equation with a highly oscillatory and weakly singular kernel
Xiang, Shuhuang
Zhang, Qingyang
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2023, 456
[10] WEAKLY SINGULAR FREDHOLM INTEGRAL-EQUATIONS WITH DISPLACEMENT KERNELS
RICHTER, GR
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1976, 55 (01) : 32 - 42

← 1 2 3 4 5 →