Numerical stability of DQ solutions of wave problems

In this paper, the solution of one-dimensional (1D) wave problems, by means of the Iterative Differential Quadrature method is discussed in terms of stability and accuracy. The 1D-wave equation with different boundary and initial conditions is considered. The time advancing scheme is here presented in a form, particularly suitable to support the discussion about stability both by the matrix method and by the energy method. The stability analysis, performed by means of these two methods, confirms the conditionally stable nature of the method. The accuracy of the solutions is discussed too.