Partial differential equation models for continuous multidimensional systems

The description of the continuous and discrete multidimensional (MD) models in current use has not yet reached the same state of maturity as for one-dimensional systems. To proceed in that direction, we investigate the connections between certain discrete partial differential equation (PDE) models (finite-difference models, transfer function models, MD wave digital filters). The starting points are potential-flux models that are the standard form of physics-based continuous MD systems. It is shown how certain matrix operations lead to various popular PDE models. The properties of the associated matrices provide the link to the discrete PDE models mentioned above. These investigations are presented in general form along with examples for an electrical transmission line and for acoustic wave propagation