A qualitative theory for simulating distributed parameter systems

The author addresses the problem of using and simulating industrial processes as distributed parameter systems (DPSs), that is partial differential equations (PDEs). A qualitative theory of linear DPSs is developed based on multidimensional Laplace transforms. A simple graphical representation using spatial and temporal frequencies is shown to be useful in predicting the behavior of the distributed parameter system. Analogously, a discrete-time/discrete-space simulation representation is derived along with the associated sampling rules. The continuous graphical s-domain frequency tools are then converted to a discrete representation and used to determine the accuracy of the resulting discrete simulation of the given PDE. The resulting graphical tools should allow engineers to have greater understanding of the behavior of DPSs