Reduces Solution of Fredholm Integral Equation
to a System of Linear Algebraic Equation

Muntaha Khudair Abbas; Dr.Maisa'a Abid Ali

doi:https://doi.org/10.14445/22315373/IJMTT-V61P518

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 61 | Number 2 | Year 2018 | Article Id. IJMTT-V61P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V61P518

Reduces Solution of Fredholm Integral Equation to a System of Linear Algebraic Equation

Muntaha Khudair Abbas, Dr.Maisa'a Abid Ali

Citation :

Muntaha Khudair Abbas, Dr.Maisa'a Abid Ali, "Reduces Solution of Fredholm Integral Equation to a System of Linear Algebraic Equation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 61, no. 2, pp. 124-132, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V61P518

Abstract

The objective of this research is to study some types of kernel of integral equations like iterated kernel, symmetric , different and Resolved kernel and to determine the Resolved kernel for Fredholm integral equation (FIE) and Volterra integral equation (VIE). It was shown that there is relation between iterated kernel and resolvent kernel as mentioned to some examples of these kernel .,also find the solution of fredholm complete neutralization for kernel and it reduces the solution of fredholm integration neutralization to a system of linear algebraic equation ,give some problem of solving system .

Keywords

kernel, Volterra integral equation, Fredholm integral equation, linear algebraic equation.

References

[1] Kendall E. Atkinson , The numerical solution of integral equations of the second kind, Cambridge Monographs on Applied and Computational Mathematics , 1997 .
[2] L. Krassnov, Integral equation , Arab Encyclopedia, vol. 18 , MiR Moscow ,1998.
[3] Abdul J. Jerri, Introduction to integral equation with applications , Sons & John Wiley ,Inc. ,second edition , Clarkson university , New York , 1999.
[4] Hazewinke, Michie, Integral Equations , Encyclopedia of Mathematics ،Springer , 2001.
[5] Yury V. Shestopalor , Yury G.Simirnor , Division for engineering science, physics and mathematics , Karlstad University,2002 .
[6] M.D.Raisinghania , Integral equation and boundary value problems , first edition , 2007 .
[7] Mohammad S.Taleb , Approximate Analytic Methods For Solving Fredhlom Integral Equations , PhD thesis, University Sains Malaysia , 2015 .
[8] Jesse P. Francis , Differential Equation , Integral Equation , edit jan 22, 2016.