On Numerical Solution of One Class of Integral Equations of the Third Kind

被引：2

作者：

Gabbasov, N. S. ^{[1
]}

Galimova, Z. Kh ^{[2
]}

机构：

[1] Kazan Fed Univ, Naberezhnye Chelny Inst, Naberezhnye Chelny 423810, Republic Of Tat, Russia

[2] Kazan Innovat Univ, Naberezhnye Chelny Branch, Naberezhnye Chelny 423815, Republic Of Tat, Russia

来源：

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2022年 / 62卷 / 02期

关键词：

integral equation of the third kind; space of generalized functions; approximate solution; theoretical substantiation; COLLOCATION METHOD; FIXED SINGULARITIES; VERSION;

D O I：

10.1134/S0965542522020075

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A linear integral equation of the third kind with fixed singularities in the kernel is studied. For its approximate solution in the space of generalized functions, a special generalized version of the spline method is proposed and substantiated. Optimality of the method in order of accuracy is proved.

引用

页码：316 / 324

页数：9

共 19 条

[1] Bart G. R., 1973, SIAM Journal on Mathematical Analysis, V4, P609, DOI 10.1137/0504053
[2] Bzhikhatlov Kh.G., 1973, Differ. Uravn, V9, P162
[3] Case K. M., 1967, Linear Transport Theory
[4] Daugavet I. K., 1977, Introduction to the Theory of Function Approximation
[5] Special version of collocation method for integral equations of the third kind with fixed singularities in a kernel
Gabbasov N.S.
Galimova Z.K.
[J]. Russian Mathematics, 2018, 62 (5) : 16 - 22
[6] On Numerical Solving Integral Equations of the Third Kind with Singularities in a Kernel
Gabbasov, N. S.
Galimova, Z. Kh.
[J]. RUSSIAN MATHEMATICS, 2016, 60 (12) : 28 - 35
[7] A New Variant of the Subdomain Method for Integral Equations of the Third Kind with Singularities in the Kernel
Gabbasov, N. S.
Zamaliev, R. R.
[J]. RUSSIAN MATHEMATICS, 2011, 55 (05) : 8 - 13
[8] Special direct method for solving integral equations in the singular case
Gabbasov, N. S.
[J]. DIFFERENTIAL EQUATIONS, 2014, 50 (09) : 1232 - 1239
[9] A new version of the collocation method for a class of integral equations in the singular case
Gabbasov, N. S.
[J]. DIFFERENTIAL EQUATIONS, 2013, 49 (09) : 1142 - 1149
[10] Methods for solving an integral equation of the third kind with fixed singularities in the kernel
Gabbasov, N. S.
[J]. DIFFERENTIAL EQUATIONS, 2009, 45 (09) : 1370 - 1378

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