Weakly singular linear Volterra integral equations: A Nystrom method in weighted spaces of continuous functions

被引：12

作者：

Fermo, Luisa ^{[1
]}

Occorsio, Donatella ^{[2
,3
]}

机构：

[1] Univ Cagliari, Dept Math & Comp Sci, Via Osped 72, I-09124 Cagliari, Italy

[2] Univ Basilicata, Dept Math & Comp Sci, Viale Ateneo Lucano 10, I-85100 Potenza, Italy

[3] CNR Natl Res Council Italy, Naples branch, Ist Applicazioni Calcolo Mauro Picone, Via P Castellino 111, I-80131 Naples, Italy

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2022年 / 406卷

关键词：

Volterra integral equations; Nystrom method; Lagrange interpolation; Orthogonal Polynomials; 2ND KIND; UNIFORM-CONVERGENCE; COLLOCATION METHODS; PROJECTION METHODS; FREDHOLM;

D O I：

10.1016/j.cam.2021.114001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper provides a Nystrom method for the numerical solution of Volterra integral equations whose kernels contain singularities of algebraic type. It is proved that the method is stable and convergent in suitable weighted spaces. An error estimate is also given as well as several numerical tests are presented. (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：12

共 39 条

[1]

Anderssen R.S, 1977, APPL NUMERICAL SOLUT

[2]

Anderssen R.S., 1980, The Application and Numerical Solution of Integral Equations

[3]

[Anonymous], 1994, THEORY APPROXIMATION

[4]

Atkinsons K.E., 1997, CAMBRIDGE MONOGRAPHS

[5] A Nystrom interpolant for some weakly singular linear Volterra integral equations [J].

Baratella, Paola .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 231 (02) :725-734

[6] ITERATED COLLOCATION METHODS AND THEIR DISCRETIZATIONS FOR VOLTERRA INTEGRAL-EQUATIONS [J].

BRUNNER, H .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1984, 21 (06) :1132-1145

[7]

Brunner H., 2004, CAMBRIDGE MONOGRAPHS, V15

[8]

Capobianco M.R., 1997, J. Integral Equ. Appl., V9, P21

[9]

Capobianco MR, 1996, OPER THEOR, V90, P153

[10] Uniform convergence of the collocation method for Prandtl's integro-differential equation [J].

Capobianco, MR ;

Criscuolo, G ;

Junghanns, P ;

Luther, U .

ANZIAM JOURNAL, 2000, 42 :151-168

← 1 2 3 4 →