ASYMPTOTIC EXPANSIONS FOR APPROXIMATE EIGENVALUES OF INTEGRAL OPERATORS WITH NONSMOOTH KERNELS OF MULTIPLICITY m > 1

被引：1

作者：

Rane, Akshay S. ^{[1
]}

机构：

[1] Birla Inst Technol & Sci, Dept Math, KK Birla Goa Campus, Zuarinagar, Goa, India

来源：

JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS | 2019年 / 31卷 / 03期

关键词：

Fredholm integral operator; Green's function type kernels; iterated Galerkin method; multiple eigenvalue; asymptotic expansion; CONVERGENCE;

D O I：

10.1216/JIE-2019-31-3-411

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an integral operator with a kernel of the Green's function type. We prove the existence of asymptotic expansion of an eigenvalue of multiplicity m > 1, when the integral operator is approximated by the iterated Galerkin operator. This enables us to use the Richardson extrapolation to increase the order of convergence of the eigenvalue. We consider a numerical example to illustrate our theoretical results.

引用

页码：411 / 430

页数：20

共 15 条

[1] SPECTRAL CONDITION NUMBERS FOR DEFECTIVE ELEMENTS OF LINEAR-OPERATORS IN HILBERT-SPACES
AHUES, M
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 1989, 10 (9-10) : 843 - 861
[2] [Anonymous], 2001, SPECTRAL COMPUTATION
[3] CONVERGENCE RATES FOR APPROXIMATE EIGENVALUES OF COMPACT INTEGRAL-OPERATORS
ATKINSON, K
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1975, 12 (02) : 213 - 222
[4] NUMERICAL SOLUTION OF EIGENVALUE PROBLEM FOR COMPACT INTEGRAL OPERATORS
ATKINSON, KE
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 129 (03) : 458 - &
[5] Baker Christopher TH, 1977, NUMERICAL TREATMENT
[6] DEFERRED APPROACH TO LIMIT FOR EIGENVALUES OF INTEGRAL EQUATIONS
BAKER, CTH
[J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1971, 8 (01) : 1 - &
[7] CHATELIN F, 1984, J INTEGRAL EQUAT, V6, P71
[8] CHATELIN F, 1983, Spectral Approximations of Linear Operators
[9] Kulkarni R. P., 2005, Journal of Numerical Mathematics, V13, P205, DOI 10.1163/156939505774286139
[10] ASYMPTOTIC EXPANSIONS FOR APPROXIMATE EIGENVALUES OF INTEGRAL OPERATORS WITH NONSMOOTH KERNELS
Kulkarni, Rekha P.
Rane, Akshay S.
[J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2012, 33 (04) : 415 - 440

← 1 2 →

ASYMPTOTIC EXPANSIONS FOR APPROXIMATE EIGENVALUES OF INTEGRAL OPERATORS WITH NONSMOOTH KERNELS OF MULTIPLICITY m &gt; 1

ASYMPTOTIC EXPANSIONS FOR APPROXIMATE EIGENVALUES OF INTEGRAL OPERATORS WITH NONSMOOTH KERNELS OF MULTIPLICITY m > 1