Amirali, IlhameFedakar, BurcuDag, DamlaAmiraliyev, Gabil M.2025-10-112025-10-1120251687-2770https://doi.org/10.1186/s13661-025-02101-yhttps://hdl.handle.net/20.500.12684/21719This paper's objective is to introduce a numerical method for solving a neutral Volterra integro-differential equation that involves fourth- and second-order derivatives. First, the stability properties of exact solution are analyzed. To solve this problem numerically, on the uniform mesh, the finite difference method, including the composite trapezoidal rule for the integral part of the equation, is used. The method has been demonstrated to be second-order convergent in the discrete maximum norm. In order to verify the efficiency of the suggested method, two numerical examples are given.en10.1186/s13661-025-02101-yinfo:eu-repo/semantics/openAccessNeutral Volterra integro-differential equationFinite difference schemeUniform convergenceError analysisArticle202512-s2.0-105012178669WOS:001539919000001Q1Q1