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 
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/
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     author = {M. G. Mahcene and A. Khellaf and S. Lemita and M. Z. Aissaoui},
     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},
     pages = {301--312},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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