Work

Toward efficient numerical solutions of non-linear integral equations with TLD algorithm

Year: 2025

Type: article

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, linearization via the Newton-Kantorovich method, and discretization with the Nyström technique. We theoretically define the convergence conditions and illustrate the accuracy of our method on several practical examples.

Source: Izvestiya Mathematics

DOI: 10.4213/im9613e

Authors: Ilyes Sedka, Ammar Khellaf

Institutions: University of Guelma, Amar Telidji University of Laghouat, Ecole Nationale Polytechnique de Constantine

Language: English

Topic: Iterative Methods for Nonlinear Equations

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

OpenAlex ID: W4410373396

FWCI:

Cites: 13

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Related to: 10