Binary and multi-valued cellular array models of linear distributed parameter systems

Abstract

Cellular array models of linear distributed parameter systems are proposed. One of the arrays is a discrete model of diffusion systems. The cells have one-bit variables E{ 1, -1 } and change their values according to a pseudo-random walker rule. Another cellular array is a one-dimensional discrete wave propagation system. The array makes unidirectional waves with spatially distributed three-level variables E{ 1,0, -1). Numerical experiment shows that the temporally or spatially averaged behavior of these cellular arrays coincides with the solutions of original diffusion and wave equations within 2.2% of error.