Finite difference method for advanced Volterra integro-differential equation with delay

Abstract

The aim of this paper is to introduce a numerical method for advanced Volterra delay inte gro-differential equation with initial condition. A finite difference scheme on a uniform mesh using the trapezoidal formula is developed to numerically solve this problem. Additionally, demonstrated that this approach yields second-order convergence in the discrete maximum norm. The proposed method is validated through the presentation of numerical results.