Simulating Nonlinear Waves and Partial Differential Equations via CNN—Part I: Basic Techniques

T. Roska, Tibor Kozek, Leon O. Chua, Ronald Tetzlaff, Frank Puffer, Dietrich Wolf

Research output: Contribution to journalArticle

126 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)807-815
Number of pages9
JournalIEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume42
Issue number10
DOIs
Publication statusPublished - 1995

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Partial differential equations
Cellular neural networks
Ordinary differential equations
Navier Stokes equations

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Simulating Nonlinear Waves and Partial Differential Equations via CNN—Part I : Basic Techniques. / Roska, T.; Kozek, Tibor; Chua, Leon O.; Tetzlaff, Ronald; Puffer, Frank; Wolf, Dietrich.

In: IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 42, No. 10, 1995, p. 807-815.

Research output: Contribution to journalArticle

Roska, T. ; Kozek, Tibor ; Chua, Leon O. ; Tetzlaff, Ronald ; Puffer, Frank ; Wolf, Dietrich. / Simulating Nonlinear Waves and Partial Differential Equations via CNN—Part I : Basic Techniques. In: IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications. 1995 ; Vol. 42, No. 10. pp. 807-815.
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