Solution of Cauchy type singular integral equations of the first kind by using differential transform method

被引：7

作者：

Abdulkawi, M. ^{[1
]}

机构：

[1] Najran Univ, Fac Sci & Arts, Dept Math, Najran, Saudi Arabia

来源：

APPLIED MATHEMATICAL MODELLING | 2015年 / 39卷 / 08期

关键词：

Integral equation; Cauchy kernel; Convolution kernel; Degenerate kernel; Differential transform method; APPROXIMATE SOLUTION;

D O I：

10.1016/j.apm.2014.10.003

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

The differential transform method is extended to solve the Cauchy type singular integral equations (CSIEs) over a finite interval. New theorems for transformation of Cauchy singular integrals are given with proofs. Approximate solutions of CSIEs with two types of kernels, Degenerate and convolution, are obtained. The system of linear equations for characteristic equation is solved analytically. Numerical results are shown to illustrate the efficiency and accuracy of the present method. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：2107 / 2118

页数：12

共 50 条

[21] Solution of Certain Weakly Singular Integral Equations of the First Kind with Indefinite Parameters
Surai, L. A.
RUSSIAN MATHEMATICS, 2009, 53 (06) : 44 - 48
[22] Solution of certain weakly singular integral equations of the first kind with indefinite parameters
L. A. Surai
Russian Mathematics, 2009, 53 (6) : 44 - 48
[23] Solution of singular integral equations with logarithmic and Cauchy kernels
Chakrabarti, A
Sahoo, T
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 1996, 106 (03): : 261 - 270
[24] Solution of ordinary differential equations and Volterra integral equation of first and second kind with bulge and logarithmic functions using Laplace transform
Bilqees, Naila
Aslam, Adnan
Ahmed, Zulfiqar
Perveen, Zahida
INTERNATIONAL JOURNAL OF ADVANCED AND APPLIED SCIENCES, 2018, 5 (09): : 82 - 87
[25] Optimal quadrature formulas for approximate solution of the first kind singular integral equation with Cauchy kernel
Akhmedov, Dilshod M.
Shadimetov, Kholmat M.
STUDIA UNIVERSITATIS BABES-BOLYAI MATHEMATICA, 2022, 67 (03): : 633 - 651
[26] Application of Chebyshev Polynomials to the Approximate Solution of Singular Integral Equations of the First Kind with Cauchy Kernel on the Real Half-line
Shali, J. Ahmadi
Akbarfam, A. Jodayree
Kashfi, M.
COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS, 2013, 4 (01): : 21 - 28
[27] Singular integral equations of the second kind with generalized Cauchy-type kernels and variable coefficients
Savruk, MP
Madenci, E
Shkarayev, S
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 1999, 45 (10) : 1457 - 1470
[28] HOMOTOPY REGULARIZATION METHOD TO SOLVE THE SINGULAR VOLTERRA INTEGRAL EQUATIONS OF THE FIRST KIND
Araghi, Mohammad Ali Fariborzi
Noeiaghdam, Samad
JORDAN JOURNAL OF MATHEMATICS AND STATISTICS, 2018, 11 (01): : 1 - 12
[29] Numerical solution of certain Cauchy singular integral equations using a collocation scheme
Seifi, Ali
ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
[30] Numerical solution of certain Cauchy singular integral equations using a collocation scheme
Ali Seifi
Advances in Difference Equations, 2020

← 1 2 3 4 5 →