In this paper, we introduce efficient and simple superconvergent postprocessing techniques for the \(C^0\) - and \(C^1\) -continuous Petrov-Galerkin (CPG) methods applied to second-order Volterra integro-differential equations. These techniques can be applied independently to each local time interval, with the computational cost being negligible compared to that of obtaining the \(C^0\) - and \(C^1\) -CPG approximations. Theoretical analysis begins with the establishment of a priori error estimates for the \(C^0\) - and \(C^1\) -CPG methods, as well as superconvergence estimates at the nodal points. Furthermore, for smooth solutions, we prove that the postprocessing techniques improve the convergence rates of the \(L^2\) -, \(H^1\) -, and \(L^\infty\) -errors of the \(C^0\) - and \(C^1\) -CPG methods by one order. Numerical experiments not only verify the theoretical results but also demonstrate the effectiveness of the proposed postprocessing techniques for handling problems with weakly singular solutions.
