Numerical methods for Fredholm integral equations with singular right-hand sides

被引：18

作者：

Fermo, L. ^{[1
]}

Russo, M. G. ^{[1
]}

机构：

[1] Univ Basilicata, Dept Math & Comp Sci, I-85100 Potenza, Italy

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2010年 / 33卷 / 03期

关键词：

Fredholm integral equations; Projection methods; Nystrom method; LAGRANGE INTERPOLATION; SMOOTHING TRANSFORMATION; POLYNOMIAL COLLOCATION; PROJECTION METHODS; SPACES; KERNELS;

D O I：

10.1007/s10444-009-9137-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Fredholm integral equations with the right-hand side having singularities at the endpoints are considered. The singularities are moved into the kernel that is subsequently regularized by a suitable one-to-one map. The Nystrom method is applied to the regularized equation. The convergence, stability and well conditioning of the method is proved in spaces of weighted continuous functions. The special case of the weakly singular and symmetric kernel is also investigated. Several numerical tests are included.

引用

页码：305 / 330

页数：26

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