Toward efficient numerical solutions of non-linear integral equations with TLD algorithm
- Authors: Sedka I.1,2,3, Khellaf A.3,4
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Affiliations:
- Université Amar Telidji Laghouat, Algeria
- Université 8 Mai 1945 Guelma, Algeria
- Laboratoire de Mathématiques Appliquées et de Modélisation (LMAM)
- École Nationale Polytechnique de Constantine,Algeria
- Issue: Vol 89, No 2 (2025)
- Pages: 128-145
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/303950
- DOI: https://doi.org/10.4213/im9613
- ID: 303950
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Abstract
This study focuses on a specific type of non-linear second-order integral equations defined over a considerable interval. We propose a new numerical method, the TLD, in three phases: transformation of the equation, linearizationvia the Newton–Kantorovich method, and discretization withthe Nyström technique. We theoretically define the convergence conditions and illustrate the accuracy of our method on several practical examples.
About the authors
Ilyes Sedka
Université Amar Telidji Laghouat, Algeria; Université 8 Mai 1945 Guelma, Algeria; Laboratoire de Mathématiques Appliquées et de Modélisation (LMAM)
Email: di_sedka@esi.dz
Ammar Khellaf
Laboratoire de Mathématiques Appliquées et de Modélisation (LMAM); École Nationale Polytechnique de Constantine,Algeria
Author for correspondence.
Email: amarlasix@gmail.com
PhD, Associate professor
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