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Minggu, Oktober 28, 2007

Numerical Vs Chaos

This paper tries to explain some results
of researches in answering the question of “ what
is chaos? “. Chaos as characteristic of a system is
defined as “the system that is susceptible to initial
condition so that the result is too much
This research tries to define the cause of chaotic
system. To answer the question, the investigators
consider (Xn, X n+1) plane.

From above study, it can be explained
that iteration method contribute to chaotic solution
Some numerical method contain problems:
iteration computation, error sampling frequency,
rounding the result. To overcome those iteration,
error sampling and rounding the result problems,
one must provide non iterating method. It is known
that neural network, fuzzy logic, cellular automata,
etc are non-iterating method such as Euler,
Predictor-Corrector, etc. Neural network, fuzzy
logic and cellular automata are known as
competent universal approximator as well as
adaptive method.
Equations from universal approximation can be
used to solve numerical problem of ODE and
PDE. By minimizing the three numerical problems
one can be sure that computing numerical
process do not cause chaotic system.

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