A novel method with error analysis for the numerical solution of a logarithmic singular Fredholm integral equation

This article attempts to investigate the numerical solution of a weakly singular Fredholm integral equation of the first kind, involving a logarithmic singularity in the reproducing kernel Hilbert space W 2 3 [ 0 , b ] . The approximate solution is represented in the form of series including finite...

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Bibliographic Details
Published in:Afrika mathematica 2023-06, Vol.34 (2), Article 33
Main Authors: Beyrami, Hossein, Lotfi, Taher
Format: Article
Language:English
Subjects:
Applications of Mathematics
Error analysis
Fredholm equations
Hilbert space
History of Mathematical Sciences
Integral equations
Logarithms
Mathematics
Mathematics and Statistics
Mathematics Education
Series (mathematics)
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Summary:This article attempts to investigate the numerical solution of a weakly singular Fredholm integral equation of the first kind, involving a logarithmic singularity in the reproducing kernel Hilbert space W 2 3 [ 0 , b ] . The approximate solution is represented in the form of series including finite number of terms. Convergence rate of the approximate solution is studied using error analysis. Numerical examples carried out to demonstrate the error analysis estimates.
ISSN:1012-9405
2190-7668
DOI:10.1007/s13370-023-01073-5