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.
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页数：12
相关论文
共 39 条
[11]   SOLVING VOLTERRA INTEGRAL EQUATIONS OF THE SECOND KIND BY SIGMOIDAL FUNCTIONS APPROXIMATION [J].
Costarelli, Danilo ;
Spigler, Renato .
JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2013, 25 (02) :193-222
[12]   Projection methods and condition numbers in uniform norm for Fredholm and Cauchy singular integral equations [J].
De Bonis, M. C. ;
Mastroianni, G. .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2006, 44 (04) :1351-1374
[13]   Filtered interpolation for solving Prandtl's integro-differential equations [J].
De Bonis, M. C. ;
Occorsio, D. ;
Themistoclakis, W. .
NUMERICAL ALGORITHMS, 2021, 88 (02) :679-709
[14]  
De Bonis MC, 2011, RIV MAT UNIV PARMA, V2, P29
[15]   Quadrature methods for integro-differential equations of Prandtl's type in weighted spaces of continuous functions [J].
De Bonis, Maria Carmela ;
Occorsio, Donatella .
APPLIED MATHEMATICS AND COMPUTATION, 2021, 393
[16]  
Ditzian Z., 1987, MODULI SMOOTHNESS
[17]   A Nystrom method for mixed boundary value problems in domains with corners [J].
Fermo, L. ;
Laurita, C. .
APPLIED NUMERICAL MATHEMATICS, 2020, 149 :65-82
[18]   Numerical methods for Fredholm integral equations with singular right-hand sides [J].
Fermo, L. ;
Russo, M. G. .
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2010, 33 (03) :305-330
[19]   VOLTERRA INTEGRAL EQUATIONS WITH HIGHLY OSCILLATORY KERNELS: A NEW NUMERICAL METHOD WITH APPLICATIONS [J].
Fermo, Luisa ;
Van Der Mee, Cornelis .
ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS, 2021, 54 :333-354
[20]  
Fermo L, 2021, DOLOMIT RES NOTES AP, V14, P12
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