A note on three numerical procedures to solve Volterra integro-differential equations in structural analysis

In this paper, three numerical methods to solve Volterra integro-differential equations containing rational functions are discussed. The first one is the Differential Quadrature Method and, to the best knowledge of the author, it has never been applied to this kind of problem; the second one is a new version of the Iterative Differential Quadrature method, a method proposed by the author some years ago to solve problems in space–time domains, revised herein for the single space variable problem; the third one is a numerical Picard-like method, proposed herein to combine successive approximations with numerical integration. Stability and convergence of the second and the third method are discussed. The three methods have been applied to solve a real world problem in the field of the structural engineering and the numerical results compared.