A second-order numerical method to the third order neutral Volterra integro-differential equations

In 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.