Winter 2022 A PROJECTION METHOD FOR VOLTERRA INTEGRAL EQUATIONS IN WEIGHTED SPACES OF CONTINUOUS FUNCTIONS
Teresa Diogo, Luisa Fermo, Donatella Occorsio
J. Integral Equations Applications 34(4): 433-448 (Winter 2022). DOI: 10.1216/jie.2022.34.433

Abstract

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.

Citation

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Teresa Diogo. Luisa Fermo. Donatella Occorsio. "A PROJECTION METHOD FOR VOLTERRA INTEGRAL EQUATIONS IN WEIGHTED SPACES OF CONTINUOUS FUNCTIONS." J. Integral Equations Applications 34 (4) 433 - 448, Winter 2022. https://doi.org/10.1216/jie.2022.34.433

Information

Received: 23 June 2021; Revised: 15 March 2022; Accepted: 15 March 2022; Published: Winter 2022
First available in Project Euclid: 10 January 2023

zbMATH: 1515.65326
MathSciNet: MR4531465
Digital Object Identifier: 10.1216/jie.2022.34.433

Subjects:
Primary: 45A05 , 45D05 , 65R20

Keywords: Lagrange interpolation , projection methods , Volterra integral equations

Rights: Copyright © 2022 Rocky Mountain Mathematics Consortium

Vol.34 • No. 4 • Winter 2022
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