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3)Updating
Ω
S
1
(
t
+1)is performed according to (15)resulting in
Ω
B
1
(
t
+1).
4)
Ω
B
1
(
t
+ 1)is averaged according to (2)to obtain
Ω
R
1
(
t
+1).
In Fig.2 some snapshots of the obtained CA evolution are shown.
5 Conclusion
A method of construction a CA, whose evolution simulates spatial dynamics
given as a PDE. The resulting CA is a paradigm of fine-grained parallel compu-
tational model, intended for being included in a unified technology for parallel
programming. Apart from the inherent parallelism the resulting CA model has
some advantages derived from discreteness of the standard part, which provides
the absence of rounding-off errors and improvement of computational stability.
As for the total e
%
ciency of the simulation by the obtained probabilistic CA
as compared with known numerical methods, in this stage it is possible to make
a tentative qualitative estimates. The quantitative ones may be made after a
long and hard work both of theoretical and experimental types. Nevertheless,
the minor experience gained during the proposed method investigation enables
us to believe that the proposed method is promising for natural phenomena
simulation.
Acknowledgment.
This work is supported by Russian Fund of Basic Research,
grant 00-01-00026.
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