On the regularization of a class of integral equations of the first kind whose kernels are discontinuous on the diagonals

被引：0

作者：

Khromov, A. P. ^{[1
]}

Khromova, G. V. ^{[1
]}

机构：

[1] Saratov NG Chernyshevskii State Univ, Ul Astrakhanskaya 83, Saratov 410012, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2012年 / 52卷 / 08期

基金：

俄罗斯基础研究基金会;

关键词：

integral equation of the first kind; regularization method; involution; convergence; Lavrent'ev method; Dirac system;

D O I：

10.1134/S0965542512080064

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For a class of integral equations of the first kind whose kernels are discontinuous on the diagonals, the convergence of the Lavrent'ev regularization method is proved by using methods of the spectral theory of integral operators. These methods lead to a special Dirac system, and finding the asymptotics of fundamental solutions is an important part of the proof.

引用

页码：1079 / 1088

页数：10

共 50 条

[1] On the regularization of a class of integral equations of the first kind whose kernels are discontinuous on the diagonals
A. P. Khromov
G. V. Khromova
[J]. Computational Mathematics and Mathematical Physics, 2012, 52 : 1079 - 1088
[2] To the theory of volterra integral equations of the first kind with discontinuous kernels
Apartsin, A. S.
[J]. COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2016, 56 (05) : 810 - 825
[3] To the theory of volterra integral equations of the first kind with discontinuous kernels
A. S. Apartsin
[J]. Computational Mathematics and Mathematical Physics, 2016, 56 : 810 - 825
[4] Solution to the Volterra Integral Equations of the First Kind with Discontinuous Kernels
Sidorov, D. N.
[J]. BULLETIN OF THE SOUTH URAL STATE UNIVERSITY SERIES-MATHEMATICAL MODELLING PROGRAMMING & COMPUTER SOFTWARE, 2012, (12): : 44 - 52
[5] Numeric solution of Volterra integral equations of the first kind with discontinuous kernels
Muftahov, Ildar
Tynda, Aleksandr
Sidorov, Denis
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2017, 313 : 119 - 128
[6] On a class of integral equations with discontinuous kernels
Langer, Rudolph E.
Brown, Eleanor P.
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1927, 29 (1-4) : 683 - 715
[7] NUMERICAL APPROXIMATION OF FIRST KIND VOLTERRA CONVOLUTION INTEGRAL EQUATIONS WITH DISCONTINUOUS KERNELS
Davies, Penny J.
Duncan, Dugald B.
[J]. JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2017, 29 (01) : 41 - 73
[8] On the regularization of Fredholm integral equations of the first kind
De Micheli, E
Magnoli, N
Viano, GA
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1998, 29 (04) : 855 - 877
[9] Regularization of Some Integral Equations of the First Kind
Malaspina, Angelica
[J]. NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS I-III, 2010, 1281 : 916 - 919
[10] Legendre polynomials approximation method for solving Volterra integral equations of the first kind with discontinuous kernels
Amirkhizi, Simin Aghaei
Mahmoudi, Yaghoub
Shamloo, Ali Salimi
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2022, 53 (02): : 492 - 504

← 1 2 3 4 5 →