Nonlinear Volterra integro-differential equations incorporating a delay term using Picard iterated method

In the context of this study, we focus on the Volterra integro-differential equation incorporating a delay term. Employing a Picard iteration scheme, we establish the existence and uniqueness of the solution, presenting the quadrature method as a tool for numerically approximating the analytical solution. Our investigation contributes to the comprehensive understanding of nonlinear Volterra integro-differential equations with delay terms. We verify the convergence of our numerical approximation method, and we provide two numerical examples, ensuring the precision of our findings. Through, varying the delay term, and underscore its substantial influence on the equation’s solution.