A new method for solving Hilbert type singular integral equations

被引：8
|
作者：
Chen, Zhong [1 ]
Zhou, YongFang [2 ,3 ]
机构：
[1] Harbin Inst Tech, Dept Math, Wei Hai 264209, Shan Dong, Peoples R China
[2] Harbin Inst Tech, Dept Math, Harbin 150001, Hei Long Jiang, Peoples R China
[3] Heilongjiang Inst Sci & Tech, Dept Math & Mech, Harbin 150027, Hei Long Jiang, Peoples R China
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 218卷 / 02期
关键词：
Hilbert type singular integral equations; Reproducing kernel space; Approximate solution;
D O I：
10.1016/j.amc.2011.05.078
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A simple method for solving Hilbert type singular integral equations is proposed. Using the reproducing kernel as the basis of W-2(1)[0,2 pi], the singularity of the considered equation is removed skillfully. Since the problem is discussed in space W-2(1)[0,2 pi], which only require the absolute continuity of the considered function, our method is effective not only for smooth solutions, but also for non-smooth solutions. The final numerical examples show the efficiency of the proposed method. (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：406 / 412
页数：7
相关论文
共 50 条
  • [1] A Direct Method of Solving Singular Integral Equations with the Hilbert Kernel
    Kadushin, V. P.
    Shakirov, A. I.
    RUSSIAN MATHEMATICS, 2009, 53 (06) : 53 - 57
  • [2] A direct method of solving singular integral equations with the Hilbert kernel
    V. P. Kadushin
    A. I. Shakirov
    Russian Mathematics, 2009, 53 (6) : 53 - 57
  • [3] A new constructive method for solving singular integral equations
    Aliev, R. A.
    MATHEMATICAL NOTES, 2006, 79 (5-6) : 749 - 770
  • [4] A new constructive method for solving singular integral equations
    R. A. Aliev
    Mathematical Notes, 2006, 79 : 749 - 770
  • [5] A new method for solving Cauchy type singular integral equations of the second kind
    Chen, Zhong
    Wang, CuiHua
    Zhou, YongFang
    INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, 2010, 87 (09) : 2076 - 2087
  • [6] An efficient algorithm for solving Hilbert type singular integral equations of the second kind
    Chen, Zhong
    Zhou, YongFang
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (04) : 632 - 640
  • [7] An analytical method for solving singular integral equations of Abel type
    Singh, Koushlendra K.
    Pandey, Rajesh K.
    Mandal, B. N.
    Dubey, Nikita
    INTERNATIONAL CONFERENCE ON MODELLING OPTIMIZATION AND COMPUTING, 2012, 38 : 2726 - 2738
  • [8] Line element method of solving singular integral equations
    Samanta, Anushree
    Chakraborty, Rumpa
    Banerjea, Sudeshna
    INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2022, 53 (02): : 528 - 541
  • [9] Wavelet Galerkin method for solving singular integral equations
    Maleknejad, K.
    Nosrati, M.
    Najafi, E.
    COMPUTATIONAL & APPLIED MATHEMATICS, 2012, 31 (02): : 373 - 390
  • [10] A SIMPLE METHOD OF SOLVING SINGULAR INTEGRAL EQUATIONS NUMERICALLY
    ROBINSON, AH
    FERZIGER, JH
    TRANSACTIONS OF THE AMERICAN NUCLEAR SOCIETY, 1969, 12 (01): : 142 - &
12345