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https://doi.org/10.64837/gsa.9...
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SOLVING VOLTERRA-FREDHOLM INTEGRAL EQUATIONS BY LINEAR SPLINE FUNCTION

Authors: SARFRAZ H. SALIM; ROSTAM K. SAEED; KARWAN H.F.JWAMER;

SOLVING VOLTERRA-FREDHOLM INTEGRAL EQUATIONS BY LINEAR SPLINE FUNCTION

Abstract

This study determines the numerical solution of linear mixed Volterra-Fredholm integral equations of the second kind using the linear spline function. The proposed method is based on using the unknown function’s linear spline function at an arbitrary point and converting the Volterra-Fredholm integral equation into a system of linear equations with regard to the unknown function using the integration method. By solving the given system, an approximate solution can be easily established. This is done with the help of a computer program that uses the Python code program version 3.9. Furthermore, we demonstrated theoretical results on the method’s uniqueness and convergence analyses.

Keywords

Volterra Integral Equation, Fredholm Integral Equation, Spline Function.

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selected citations
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This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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