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Analytical discussion for the mixed integral equations
Journal of Fixed Point Theory and Applications • 2018
Publication Information
Authors
M. E. Nasr; M. A. Abdel-Aty
Keywords
Banach space; Volterra–Fredholm integral equation; degenerate kernel method.
Journal
Journal of Fixed Point Theory and Applications
Publisher
Springer International Publishing AG, part of Springer Nature 2018
Volume
20
Issue
3
Pages
Not Available
publication.type
International
Paper Link
Open Link
Supplementary Materials
Not Available
Abstract
This paper presents a numerical method for the solution of a
Volterra–Fredholm integral equation in a Banach space. Banachs fixed point theorem is used to prove the existence and uniqueness of the solution.
To find the numerical solution, the integral equation is reduced to
a system of linear Fredholm integral equations, which is then solved numerically using the degenerate kernel method. Normality and continuity of the integral operator are also discussed. The numerical examples in Sect. 5 illustrate the applicability of the theoretical results.
Volterra–Fredholm integral equation in a Banach space. Banachs fixed point theorem is used to prove the existence and uniqueness of the solution.
To find the numerical solution, the integral equation is reduced to
a system of linear Fredholm integral equations, which is then solved numerically using the degenerate kernel method. Normality and continuity of the integral operator are also discussed. The numerical examples in Sect. 5 illustrate the applicability of the theoretical results.