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

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.

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