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Continuous Valued Cellular Automata for Nonlinear Wave Equations

Daniel N. Ostrov
Department of Mathematics
Santa Clara University
Santa Clara CA, 95053 - Rudy Rucker
Department of Mathematics
and Computer Science
San Jose State University
San Jose CA, 95192

Paper completed July 7, 1997

Reproduced from Complex Systems 10 (1196) 91-119 [Actual publication date Fall 97]


In 1955, E. Fermi, J. Pasta, and S. Ulam investigated quadratic and cubic schemes for numerically simulating nonlinear waves. In our paper, we derive the partial differential equations corresponding to the Fermi-Pasta-Ulam schemes, present a discussion of the accuracy and stability of different schemes for the equations, and implement the schemes as continuous-valued celluar automata. Some illustrative runs of the shareware CAPOW cellular automata simulator are presented which demonstrate the behavior of the different schemes both in stable and unstable domains. These runs include a confirmation of an observation of Fermi, Pasta and Ulam regarding the approximate temporal periodicity of the quadratic and cubic nonlinear wave equations.

Copyright (C) 1996 Complex Systems, Inc.

Rudy Rucker
Sat May 9 20:21:15 MET DST 1998