SIMULATING NONLINEAR-WAVES AND PARTIAL-DIFFERENTIAL EQUATIONS VIA CNN.1. BASIC TECHNIQUES

Cellular neural networks (CNNs)-a paradigm for locally connected analo g array-computing structures-are considered for solving partial differ ential equations (PDE's) and systems of ordinary differential equation s (DDE's). The relationship between various implementations of nonanal ytical PDE solvers is discussed. The applicability of CNNs is shown by three examples of nonlinear PDE implementations: a reaction-diffusion type system, Burgers' equation, and a form of the Navier-Stokes equat ion in a two-dimensional setting.