This presentation concerns a numerical method for the simulation of wave propagation.
First part deals with one-dimensional wave problems.
Some important practical requirements for finite difference methods are formulated. To satisfy these requirements, the proposed method is based on two key features. First, the approximate solution is represented as a set of exponential functions with variable coefficients in every zone on a computational grid. Second, assuming that the physical parameters are constant in every zone the wave equation is represented as two advection equations for Riemann invariants. Numerical results for different problems of wave propagation in comparison with the analytical solutions are presented.