Analytical discussion for the mixed integral equations

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 Fredho...

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Bibliographic Details
Published inJournal of fixed point theory and applications Vol. 20; no. 3; pp. 1 - 19
Main Authors Nasr, M. E., Abdel-Aty, M. A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2018
Springer Nature B.V
Subjects
Analysis
Banach spaces
Existence theorems
Fixed points (mathematics)
Integral equations
Mathematical analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Normality
Numerical methods
Operators (mathematics)
45A05
46B07
degenerate kernel method
65R20
Banach space
Volterra–Fredholm integral equation
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Summary: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.
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-018-0589-3