Simulating nonlinear waves and partial differential equations via CNN. I. Basic techniques

Abstract

Cellular neural networks (CNNs)-a paradigm for locally connected analog array-computing structures-are considered for solving partial differential equations (PDE's) and systems of ordinary differential equations (ODE's). The relationship between various implementations of nonanalytical 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 equation in a two-dimensional setting.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>