<s>
Continuous	B-General_Concept
Simulation	I-General_Concept
refers	O
to	O
simulation	O
approaches	O
where	O
a	O
system	O
is	O
modeled	O
with	O
the	O
help	O
of	O
variables	O
that	O
change	O
continuously	O
according	O
to	O
a	O
set	O
of	O
differential	O
equations	O
.	O
</s>
<s>
It	O
is	O
notable	O
as	O
one	O
of	O
the	O
first	O
uses	O
ever	O
put	O
to	O
computers	O
,	O
dating	O
back	O
to	O
the	O
Eniac	B-Device
in	O
1946	O
.	O
</s>
<s>
Since	O
that	O
time	O
continuous	B-General_Concept
simulation	I-General_Concept
has	O
been	O
proven	O
invaluable	O
in	O
military	O
and	O
private	O
endeavors	O
with	O
complex	O
systems	O
.	O
</s>
<s>
In	O
continuous	B-General_Concept
simulation	I-General_Concept
,	O
continuously	O
changing	O
state	O
variables	O
of	O
a	O
system	O
are	O
modeled	O
by	O
differential	O
equations	O
.	O
</s>
<s>
However	O
,	O
in	O
digital	O
computing	O
,	O
real	O
numbers	O
cannot	O
be	O
faithfully	O
represented	O
and	O
differential	O
equations	O
can	O
only	O
be	O
solved	O
numerically	O
with	O
approximate	O
algorithms	O
(	O
like	O
the	O
method	B-Algorithm
of	I-Algorithm
Euler	I-Algorithm
or	O
Runge	B-Algorithm
–	I-Algorithm
Kutta	I-Algorithm
)	O
using	O
some	O
form	O
of	O
discretization	O
.	O
</s>
<s>
Consequently	O
,	O
digital	O
computers	O
cannot	O
run	O
truly	O
continuous	B-General_Concept
simulations	I-General_Concept
.	O
</s>
<s>
Only	O
analog	O
computers	O
can	O
run	O
truly	O
continuous	B-General_Concept
simulations	I-General_Concept
.	O
</s>
<s>
Discrete	B-General_Concept
event	I-General_Concept
simulation	I-General_Concept
,	O
on	O
the	O
other	O
hand	O
,	O
changes	O
state	O
variables	O
only	O
in	O
response	O
to	O
events	O
,	O
typically	O
using	O
next-event	O
time	O
progression	O
.	O
</s>
<s>
Continuous	O
dynamic	O
systems	O
can	O
only	O
be	O
captured	O
by	O
a	O
continuous	B-General_Concept
simulation	I-General_Concept
model	O
,	O
while	O
discrete	O
dynamic	O
systems	O
can	O
be	O
captured	O
either	O
in	O
a	O
more	O
abstract	O
manner	O
by	O
a	O
continuous	B-General_Concept
simulation	I-General_Concept
model	O
(	O
like	O
the	O
Lotka-Volterra	O
equations	O
)	O
or	O
in	O
a	O
more	O
realistic	O
manner	O
by	O
a	O
discrete	B-General_Concept
event	I-General_Concept
simulation	I-General_Concept
model	O
,	O
since	O
birth	O
,	O
death	O
and	O
predator-prey	O
encounters	O
are	O
discrete	O
events	O
.	O
</s>
<s>
When	O
using	O
a	O
continuous	B-General_Concept
simulation	I-General_Concept
model	O
of	O
the	O
discrete	O
dynamic	O
system	O
of	O
a	O
population	O
of	O
animals	O
,	O
one	O
may	O
get	O
results	O
like	O
23.7	O
animals	O
,	O
which	O
first	O
have	O
to	O
be	O
rounded	O
for	O
making	O
sense	O
.	O
</s>
<s>
Using	O
a	O
discrete	B-General_Concept
event	I-General_Concept
simulation	I-General_Concept
makes	O
it	O
necessary	O
to	O
have	O
an	O
occurring	O
event	O
to	O
change	O
the	O
number	O
of	O
sales	O
.	O
</s>
<s>
In	O
contrast	O
to	O
this	O
the	O
continuous	B-General_Concept
simulation	I-General_Concept
has	O
a	O
smooth	O
and	O
steady	O
development	O
in	O
its	O
number	O
of	O
sales	O
.	O
</s>
<s>
A	O
continuous	B-General_Concept
simulation	I-General_Concept
of	O
sales	O
implies	O
the	O
possibility	O
of	O
fractional	O
sales	O
e.g.	O
</s>
<s>
For	O
that	O
reason	O
,	O
a	O
continuous	B-General_Concept
simulation	I-General_Concept
of	O
sales	O
does	O
not	O
faithfully	O
model	O
reality	O
but	O
may	O
nevertheless	O
capture	O
the	O
system	O
's	O
dynamics	O
approximately	O
.	O
</s>
<s>
Continuous	B-General_Concept
simulations	I-General_Concept
are	O
based	O
on	O
a	O
set	O
of	O
differential	O
equations	O
.	O
</s>
<s>
The	O
set	O
of	O
differential	O
equations	O
can	O
be	O
formulated	O
in	O
a	O
conceptual	B-Application
model	I-Application
representing	O
the	O
system	O
on	O
an	O
abstract	O
level	O
.	O
</s>
<s>
In	O
order	O
to	O
develop	O
the	O
conceptual	B-Application
model	I-Application
2	O
approaches	O
are	O
feasible	O
:	O
</s>
<s>
A	O
widely	O
known	O
example	O
for	O
a	O
continuous	B-General_Concept
simulation	I-General_Concept
conceptual	B-Application
model	I-Application
is	O
the	O
"	O
predator/prey	O
model	O
"	O
.	O
</s>
<s>
A	O
continuous	B-General_Concept
simulation	I-General_Concept
of	O
population	O
dynamics	O
represents	O
an	O
approximation	O
of	O
the	O
population	O
effectively	O
fitting	O
a	O
curve	O
to	O
a	O
finite	O
set	O
of	O
measurements/points	O
.	O
</s>
<s>
In	O
continuous	B-General_Concept
simulation	I-General_Concept
,	O
the	O
continuous	O
time	O
response	O
of	O
a	O
physical	O
system	O
is	O
modeled	O
using	O
ODEs	O
,	O
embedded	O
in	O
a	O
conceptual	B-Application
model	I-Application
.	O
</s>
<s>
The	O
Linear	B-Algorithm
Multistep	I-Algorithm
family	O
.	O
</s>
<s>
Numerical	O
integration	O
methods	O
such	O
as	O
Runge	B-Algorithm
Kutta	I-Algorithm
,	O
or	O
Bulirsch-Stoer	B-Algorithm
could	O
be	O
used	O
to	O
solve	O
this	O
particular	O
system	O
of	O
ODEs	O
.	O
</s>
<s>
To	O
speed	O
creation	O
of	O
continuous	B-General_Concept
simulations	I-General_Concept
you	O
can	O
use	O
graphical	O
programming	O
software	O
packages	O
like	O
VisSim	B-Application
or	O
Simcad	B-Application
Pro	I-Application
.	O
</s>
<s>
Such	O
graphical	O
simulation	B-Application
software	I-Application
can	O
be	O
run	O
in	O
real-time	O
and	O
used	O
as	O
a	O
training	O
tool	O
for	O
managers	O
and	O
operators	O
.	O
</s>
<s>
Indeed	O
,	O
much	O
of	O
modern	O
technology	O
that	O
we	O
enjoy	O
today	O
would	O
not	O
be	O
possible	O
without	O
continuous	B-General_Concept
simulation	I-General_Concept
.	O
</s>
