New results in numerically integrating PDES by the wave digital approach

Physical systems described by ordinary or partial differential equations can be modelled advantageously by the wave digital approach, i.e., by a generalization of the techniques known from one- and multi-dimensional wave digital filtering. Such a modelling leads to numerical algorithms that have a number of attractive properties such as high accuracy, massive parallelism, high robustness against the influences of numerical inaccuracies, full locality and thus simple possibilities for taking into account nonuniform parameters and nonlinearities, as well as very general boundary conditions and shapes etc. This has been confirmed by recent investigations that concern, for example, coupled and nonuniform-transmission lines as well as transmisson lines with frequency-dependent and nonlinear terminations. Several results about this are presented in the paper