A piecewise exponential method for the numerical simulation of wave propagation

A finite difference scheme for the numerical simulation of linear wave propagation is presented. The proposed method is based on the solution of Riemann problem and the special representation of an approximate solution in every difference interval. The resulting scheme produces relatively small dissipation and dispersion of an approximate solution for all admissible values of the Courant number and retains the monotonicity of the exact solution. Some numerical results obtained for wave propagation in an inhomogeneous rod are discussed.