<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
order	B-Algorithm
of	I-Algorithm
accuracy	I-Algorithm
quantifies	O
the	O
rate	B-Architecture
of	I-Architecture
convergence	I-Architecture
of	O
a	O
numerical	B-General_Concept
approximation	I-General_Concept
of	O
a	O
differential	O
equation	O
to	O
the	O
exact	O
solution	O
.	O
</s>
<s>
Consider	O
a	O
numerical	B-General_Concept
approximation	I-General_Concept
,	O
where	O
is	O
a	O
parameter	O
characterizing	O
the	O
approximation	O
,	O
such	O
as	O
the	O
step	O
size	O
in	O
a	O
finite	O
difference	O
scheme	O
or	O
the	O
diameter	O
of	O
the	O
cells	O
in	O
a	O
finite	B-Application
element	I-Application
method	I-Application
.	O
</s>
<s>
The	O
numerical	B-General_Concept
solution	I-General_Concept
is	O
said	O
to	O
be	O
th-order	O
accurate	O
if	O
the	O
error	O
is	O
proportional	O
to	O
the	O
step-size	O
to	O
the	O
th	O
power	O
:	O
</s>
<s>
This	O
definition	O
is	O
strictly	O
dependent	O
on	O
the	O
norm	O
used	O
in	O
the	O
space	O
;	O
the	O
choice	O
of	O
such	O
norm	O
is	O
fundamental	O
to	O
estimate	O
the	O
rate	B-Architecture
of	I-Architecture
convergence	I-Architecture
and	O
,	O
in	O
general	O
,	O
all	O
numerical	O
errors	O
correctly	O
.	O
</s>
<s>
The	O
size	O
of	O
the	O
error	O
of	O
a	O
first-order	B-Algorithm
accurate	I-Algorithm
approximation	O
is	O
directly	O
proportional	O
to	O
.	O
</s>
