A PROJECTION METHOD FOR VOLTERRA INTEGRAL EQUATIONS IN WEIGHTED SPACES OF CONTINUOUS FUNCTIONS

被引：4

作者：

Diogo, Teresa ^{[1
]}

Fermo, Luisa ^{[2
]}

Occorsio, Donatella ^{[3
,4
]}

机构：

[1] Univ Lisbon, Ctr Computat & Stochast Math CEMAT IST ULisboa, Inst Super Tecn, Dept Math, Lisbon, Portugal

[2] Univ Cagliari, Dept Math & Comp Sci, Cagliari, Italy

[3] Univ Basilicata, Dept Math Comp Sci & Econ, Potenza, Italy

[4] Natl Res Council CNR Italy, Ist Applicaz Calcolo Mauro Picone, Naples, Italy

来源：

JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS | 2022年 / 34卷 / 04期

关键词：

Volterra integral equations; projection methods; Lagrange interpolation; HIGH-ORDER METHODS; NUMERICAL-SOLUTION; COLLOCATION METHOD; 2ND KIND; SMOOTHING TRANSFORMATION; UNIFORM-CONVERGENCE; FREDHOLM;

D O I：

10.1216/jie.2022.34.433

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the numerical treatment of second kind Volterra integral equations whose integrands present diagonal and/or endpoint algebraic singularities. A projection method based on an optimal interpolating operator is developed in the spaces of weighted continuous functions endowed with the supremum norm. In such spaces, the uniqueness of the solution is discussed and suitable conditions are determined to assure the stability and the convergence of the method. Several numerical tests are presented to show the efficiency of the method and the agreement with the theoretical estimates.

引用

页码：433 / 448

页数：16

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