Geodesic
A refinement sum-technique in an iterative scheme adapted for a linear system of integral equations to approach a Fredholm integral equation's solution
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 26 (2023) no. 3, pp. 301-312 Cet article a éte moissonné depuis la source Math-Net.Ru

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Based on the use of the geometric series theorem, we transform a linear Fredholm integral equation of the second kind defined on a large interval into an equivalent linear system of Fredholm integral equations of the second kind; then, we inflict a refinement in the way the investigated generalised iterative scheme approximates the sought-after solution. By avoiding to inverse a bounded linear operator, and computing a truncated geometric sum of the former's associated sequence of bounded linear operators instead, we notice that our approach furnishes a better performance in terms of computational time and error efficiency. 
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     title = {A refinement sum-technique in an iterative scheme adapted for a linear system of integral equations to approach a {Fredholm} integral equation's solution},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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M. G. Mahcene; A. Khellaf; S. Lemita; M. Z. Aissaoui. A refinement sum-technique in an iterative scheme adapted for a linear system of integral equations to approach a Fredholm integral equation's solution. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 26 (2023) no. 3, pp. 301-312. http://geodesic.mathdoc.fr/item/SJVM_2023_26_3_a5/

[1] Ahues M., D'Almeida F., Largillier A., Titaud O., Vasconcelos P., “An $L^1$ refined projection approximate solution of the radiation transfer equation in stellar atmospheres”, J. Compt. Appli. Math., 140 (2002), 13–26 | DOI | MR | Zbl

[2] Atkinson K.E., The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, New York, 1997 | MR | Zbl

[3] Atkinson K.E., “A personal perspective on the history of the numerical analysis of Fredholm integral equations of the second kind”, The Birth of Numerical Analysis, 2009, 53–72 | DOI | MR

[4] Atkinson K.E., Han W., Theoretical Numerical Analysis: A Functional Analysis Framework, Texts in Applied Mathematics, 39, 3rd ed., 2009 | MR | Zbl

[5] D'Almeida F., Titaud O., Vasconcelos P., “A numerical study of iterative refinement schemes for weakly singular integral equations”, App. Math. Lett., 18 (2005), 571–576 | DOI | MR | Zbl

[6] Lemita S., Guebbai H., “New process to approach linear Fredholm integral equation defined on large interval”, Asian-European J. Math., 12:01 (2017) | DOI | MR

[7] Lemita S., Guebbai H., and Aissaoui M.Z., “Generalized Jacobi method for linear bounded operators system”, Comp. Appl. Math., 37 (2018), 3967–3980 | DOI | MR | Zbl

[8] Lemita S., Guebbai H., and Khellaf A., “New version of Gauss Seidel iterative method for operators system to approach Fredholm integral equation”, Proc. 8th Intern. Conf. on Modeling Simulation and Applied Optimization (ICMSAO), IEEE, 2019 | DOI

[9] Pastore P., “The numerical treatment of Love's integral equation having very small parameter”, J. Compt. Appl. Math., 236 (2011), 1267–1281 | DOI | MR | Zbl

[10] Quarteroni A., Sacco R., Saleri F., Numerical Mathematics, Texts in Applied Mathematics, 37, 2000 | MR | Zbl

[11] Titaud O., Analyse Et résolution Numérique de Léquation de Transfert. Application au Problème des Atmosphères Stellaires, Ph.D. thesis, Université Jean Monnet-Saint-Etienne, 2001

[12] Saad Y., Iterative Methods for Sparse Linear Systems, 2nd ed., SIAM, Philadelphia, 2003 | MR | Zbl