Amirali, IlhameDag, DamlaDurmaz, Muhammet EnesAmiraliyev, Gabil M.2026-07-012026-07-0120261687-2770https://doi.org/10.1186/s13661-026-02259-zhttps://hdl.handle.net/20.500.12684/23379In this study, a second-order numerical method is proposed for solving a third-order neutral type Volterra integro-differential equation (NVIDE). The proposed method is based on finite difference approximations for the differential terms and a suitable quadrature rule for the integral term. The method is constructed on a uniform mesh and is shown to achieve second-order accuracy. Stability and convergence analyses are carried out under appropriate assumptions. A numerical experiment is presented to verify the efficiency, accuracy, and theoretical order of convergence of the proposed scheme.en10.1186/s13661-026-02259-zinfo:eu-repo/semantics/openAccess[Keyword Not Available]Article202612-s2.0-105035887221WOS:001742408400001Q1Q1