A refinement sum-technique in an iterative scheme adapted for a linear system of integral equations to approach a Fredholm integral equation's solution
Mohammed GhaГЇth Mahcene1, Ammar Khellaf2,3, Samir Lemita4,3, Mohamed Zine Aissaoui1
1Laboratory of Applied Mathematics and Modelling (LAMM) University, Guelma, Algeria
2Polytechnic National School of Constantine, Constantine, Algeria
3Laboratory of Applied Mathematics and Modelling (LAMM), Guelma, Algeria
4Higher Normal School of Ouargla, Ouargla, Algeria
Keywords: integral equations, bounded linear operators, iterative methods, Nyström method
Abstract
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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