Simulating nonlinear waves and partial differential equations via CNN - part I: Basic techniques

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...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems. 1, Fundamental theory and applications Fundamental theory and applications, 1995-01, Vol.42 (10), p.807-815
Main Authors: Roska, Tamas, Chua, Leon O, Wolf, Dietrich, Kozek, Tibor, Tetzlaff, Ronald, Puffer, Frank
Format: Article
Language:English
Online Access:Get full text
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Summary: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.
ISSN:1057-7122
DOI:10.1109/81.473590