Numerical solutions for second-order neutral volterra integro-differential equations: Stability analysis and finite difference method

This work deals with the initial-value problem for a second-order neutral Volterra integro-differential equation. First, we give the stability inequality indicating stability of the problem with respect to the right-side and initial conditions. Further, we develop a finite difference method that uses for differential part second difference derivative, for the integral part appropriate composite trapezoidal and midpoint rectangle rules followed by second-order accurate difference quantities at intermediate points. Error estimate for the approximate solution is established. In support of theoretical results, numerical results are performed by employing the proposed numerical technique.