Numerical solutions of nonlinear quadratic volterra integral equations using vieta-lucas wavelets

• Autorzy: Mehellou Abderrazak , Khirani Amina , Nadir Nadir

Identyfikatory

DOI

10.17512/jamcm.2025.2.04

• Języki publikacji: EN

Abstrakty

EN

In this article, we present a numerical approach for solving Nonlinear Quadratic Volterra Integral Equations (NQVIEs) with the collocation method using Vieta-Lucas Wavelets (VLWs) and the Legendre-Gauss Quadrature Rule (LGQR). First, we prove the existence and uniqueness of the main problem under specific conditions. Then, we apply the proposed method; the NQVIEs well be reduced to a system of nonlinear algebraic equations that can be solved by Newton’s method. We also estimate the error bound and the convergence of the presented method. Several numerical examples are mentioned in order to demonstrate its effectiveness and accuracy in solving NQVIEs.

Słowa kluczowe

EN

nonlinear quadratic Volterra integral equations; Vieta-Lucas wavelets method; collocation method; Gauss quadrature rule

PL

nieliniowe równania całkowe kwadratowe Volterry; metoda falek Vieta-Lucasa; metoda kolokacji; reguła kwadraturowa Gaussa

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2025
• Tom: Vol. 24, nr 2
• Strony: 47--60
• Opis fizyczny: Bibliogr. 20 poz., rys., tab.

Twórcy

autor

Mehellou Abderrazak

• Laboratory of Pure and Applied Mathematics, University of M’Sila University pole, Bordj Bou Arreridj road, M’Sila 28000, Algeria

autor

Khirani Amina

• Laboratory of Pure and Applied Mathematics, University of M’Sila University pole, Bordj Bou Arreridj road, M’Sila 28000, Algeria

autor

Nadir Nadir

• Laboratory of Pure and Applied Mathematics, University of M’Sila University pole, Bordj Bou Arreridj road, M’Sila 28000, Algeria

Bibliografia

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• [16] Avazzadeh, Z. (2012). A numerical approach for solving quadratic integral equations of Urysohn’s type using radial basis function. Journal of Applied & Computational Mathematics, 1(4), 1000116.
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Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).