A spline product quasi-interpolation method for weakly singular Fredholm integral equations

被引：41

作者：

Vainikko, Eero ^{[1
]}

Vainikko, Gennadi ^{[1
]}

机构：

[1] Univ Tartu, Fac Math & Comp Sci, EE-50409 Tartu, Estonia

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2008年 / 46卷 / 04期

关键词：

weakly singular integral equations; boundary singularities; spline quasi-interpolation; spline interpolation; product integration methods; Nystrom-type methods;

D O I：

10.1137/070693308

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A discrete method of accuracy O(h(m)) is constructed and justified for a class of Fredholm integral equations of the second kind with kernels that may have weak diagonal and boundary singularities. The method is based on (i) improving the boundary behavior of the kernel with the help of a change of variables, and (ii) the product integration using quasi-interpolation by smooth splines of order m.

引用

页码：1799 / 1820

页数：22

共 50 条

[11] Reproducing kernel method for a class of weakly singular Fredholm integral equations
Alvandi, Azizallah
Paripour, Mahmoud
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, 2018, 12 (04): : 409 - 414
[12] On the regularization method for Fredholm integral equations with odd weakly singular kernel
Benrabia, Noureddine
Guebbai, Hamza
COMPUTATIONAL & APPLIED MATHEMATICS, 2018, 37 (04): : 5162 - 5174
[13] On the regularization method for Fredholm integral equations with odd weakly singular kernel
Noureddine Benrabia
Hamza Guebbai
Computational and Applied Mathematics, 2018, 37 : 5162 - 5174
[14] CONVERGENCE ANALYSIS OF PRODUCT INTEGRATION METHOD FOR NONLINEAR WEAKLY SINGULAR VOLTERRA-FREDHOLM INTEGRAL EQUATIONS
Darania, Parviz
Shali, Jafer Ahmadi
SAHAND COMMUNICATIONS IN MATHEMATICAL ANALYSIS, 2015, 2 (01): : 57 - 69
[15] Smoothing Transformation and Cubic Spline Collocation for Weakly Singular Fredholm Integral Equations with Boundary Singularities
Pedas, Arvet
Vikerpuur, Mikk
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2012), VOLS A AND B, 2012, 1479 : 708 - 711
[16] Product integration methods based on discrete spline quasi-interpolants and application to weakly singular integral equations
Allouch, C.
Sablonniere, P.
Sbibih, D.
Tahrichi, M.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 233 (11) : 2855 - 2866
[17] The Cubic Spline-Collocation Method for Weakly Singular Integral Equations
A. Pedas
E. Timak
Differential Equations, 2001, 37 : 1491 - 1500
[18] Smoothing and Quadratic Spline Collocation Method for Weakly Singular Integral Equations
Pallav, Rene
Pedas, Arvet
NUMERICAL ANALYSIS AND APPLIED MATHEMATICS, VOLS 1 AND 2, 2009, 1168 : 1288 - 1291
[19] The cubic spline-collocation method for weakly singular integral equations
Pedas, A
Timak, E
DIFFERENTIAL EQUATIONS, 2001, 37 (10) : 1491 - 1500
[20] Cubic quasi-interpolation spline collocation method for solving convection-diffusion equations
Bouhiri, S.
Lamnii, A.
Lamnii, M.
MATHEMATICS AND COMPUTERS IN SIMULATION, 2019, 164 : 33 - 45

← 1 2 3 4 5 →