Discrete simulation of linear multidimensional continuous systems

Abstract

This paper presents the theoretical foundations of a new method for the discrete simulation of multidimensional systems, which are described by linear partial differential equations with constant coefficients. It is based on methods customary in linear systems theory and digital signal processing and uses a frequency-domain representation of the continuous system to be simulated. The selection of appropriate functional transformations for each variable yields an exact treatment of initial and boundary conditions. The heat-flow equation is treated as an example. For this case, a realizing structure for the simulating discrete system is given along with simulation examples.