Title :
Simulating nonlinear waves and partial differential equations via CNN. I. Basic techniques
Author :
Roska, Tamás ; Chua, Leon O. ; Wolf, Dietrich ; Kozek, Tibor ; Tetzlaff, Ronald ; Puffer, Frank
Author_Institution :
Comput. & Autom. Inst., Hungarian Acad. of Sci., Budapest, Hungary
fDate :
10/1/1995 12:00:00 AM
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
Keywords :
Navier-Stokes equations; cellular neural nets; nonlinear differential equations; partial differential equations; wave equations; Burgers equation; CNN; locally connected analog array-computing structures; nonanalytical PDE solvers; nonlinear waves; ordinary differential equations; partial differential equations; reaction-diffusion system; simulation; two-dimensional Navier-Stokes equation; CMOS technology; Cellular neural networks; Differential equations; Integrated circuit interconnections; Laboratories; Nonlinear equations; Partial differential equations; Space heating; Space technology; Very large scale integration;
Journal_Title :
Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on
