Some Considerations on Numerical Methods for Cauchy Singular Integral Equations on the Real Line

被引：0

作者：

Capobianco, Maria Rosaria ^{[1
]}

Criscuolo, Giuliana ^{[2
]}

机构：

[1] CNR, Ist Applicaz Calcolo M Picone, Sede Napoli, Via Pietro Castellino 111, I-80131 Naples, Italy

[2] Univ Napoli Federico II, Dipartimento Matemat & Applicazioni, Edificio T,Via Cintia, I-80126 Naples, Italy

来源：

MATHEMATICAL MODELLING AND ANALYSIS | 2024年 / 29卷 / 02期

关键词：

Hilbert transform; singular integral equation; Hermite weight; WEIGHTED HILBERT TRANSFORM; APPROXIMATION;

D O I：

10.3846/mma.2024.18688

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Two different direct methods are proposed to solve Cauchy singular integral equations on the real line. The aforementioned methods differ in order to be able to prove their convergence which depends on the smoothness of the known term function in the integral equation.

引用

页码：268 / 276

页数：9

共 50 条

[1] Numerical methods for some special Fredholm integral equations on the real line
De Bonis, MC
Frammartino, C
Mastroianni, G
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2004, 164 : 225 - 243
[2] Methods for solving a singular integral equation with Cauchy kernel on the real line
Gabdulkhaev, B. G.
Tikhonov, I. N.
[J]. DIFFERENTIAL EQUATIONS, 2008, 44 (07) : 980 - 990
[3] Methods for solving a singular integral equation with Cauchy kernel on the real line
B. G. Gabdulkhaev
I. N. Tikhonov
[J]. Differential Equations, 2008, 44 : 980 - 990
[4] ON SOME SINGULAR INTEGRAL EQUATIONS OF THE CAUCHY TYPE
ELLIOTT, J
[J]. ANNALS OF MATHEMATICS, 1951, 54 (02) : 349 - 370
[5] Cauchy singular integral equations in spaces of continuous functions and methods for their numerical solution
Junghanns, P
Luther, U
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 1997, 77 (1-2) : 201 - 237
[6] Numerical methods for Cauchy singular integral equations in spaces of weighted continuous functions
Mastroianni, G
Russo, MG
Themistoclakis, W
[J]. RECENT ADVANCES IN OPERATOR THEORY AND ITS APPLICATIONS: THE ISRAEL GOHBERG ANNIVERSARY VOLUME, 2005, 160 : 311 - 336
[7] Collocation methods for Cauchy singular integral equations on the interval
Junghanns, P
Rogozhin, A
[J]. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2004, 17 : 11 - 75
[8] THE COLLOCATION METHODS FOR SINGULAR INTEGRAL EQUATIONS WITH CAUCHY KERNELS
杜金元
[J]. Acta Mathematica Scientia, 2000, (03) : 289 - 302
[9] On collocation methods for nonlinear Cauchy singular integral equations
Junghanns, P
Müller, K
Rost, K
[J]. TOEPLITZ MATRICES AND SINGULAR INTEGRAL EQUATIONS: THE BERND SILBERMANN ANNIVERSARY VOL, 2002, 135 : 209 - 233
[10] The collocation methods for singular integral equations with Cauchy kernels
Du, JY
[J]. ACTA MATHEMATICA SCIENTIA, 2000, 20 (03) : 289 - 302

← 1 2 3 4 5 →