<s>
The	O
Scarborough	B-Algorithm
criterion	I-Algorithm
is	O
used	O
for	O
satisfying	O
convergence	O
of	O
a	O
solution	O
while	O
solving	O
linear	O
equations	O
using	O
an	O
iterative	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
Solutions	O
of	O
such	O
equations	O
can	O
be	O
obtained	O
numerically	B-General_Concept
,	O
at	O
discrete	O
points	O
of	O
the	O
solution	O
domain	O
(	O
e.g.	O
</s>
<s>
Numerical	B-General_Concept
solutions	I-General_Concept
based	O
on	O
the	O
integration	O
of	O
the	O
equations	O
at	O
discrete	O
control	O
volumes	O
of	O
the	O
solution	O
domain	O
(	O
for	O
example	O
the	O
Finite	B-Algorithm
Volume	I-Algorithm
Method	I-Algorithm
)	O
result	O
in	O
a	O
system	O
of	O
algebraic	O
equations	O
,	O
one	O
for	O
each	O
nodal	O
point	O
(	O
corresponding	O
to	O
a	O
particular	O
control	O
volume	O
)	O
.	O
</s>
<s>
The	O
Scarborough	B-Algorithm
criterion	I-Algorithm
formulated	O
by	O
Scarborough	O
(	O
1958	O
)	O
,	O
can	O
be	O
expressed	O
in	O
terms	O
of	O
the	O
values	O
of	O
the	O
coefficients	O
of	O
the	O
discretised	O
equations	O
:	O
</s>
<s>
The	O
satisfaction	O
of	O
this	O
criterion	O
ensures	O
that	O
the	O
equations	O
will	O
be	O
converged	O
by	O
at	O
least	O
one	O
iterative	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
If	O
Scarborough	B-Algorithm
criterion	I-Algorithm
is	O
not	O
satisfied	O
then	O
Gauss	B-Algorithm
–	I-Algorithm
Seidel	I-Algorithm
method	I-Algorithm
iterative	I-Algorithm
procedure	I-Algorithm
is	O
not	O
guaranteed	O
to	O
converge	O
a	O
solution	O
.	O
</s>
<s>
If	O
this	O
criterion	O
is	O
satisfied	O
then	O
it	O
means	O
equation	O
will	O
be	O
converged	O
by	O
at	O
least	O
one	O
iterative	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
The	O
Scarborough	B-Algorithm
criterion	I-Algorithm
is	O
used	O
as	O
a	O
sufficient	O
condition	O
for	O
convergent	O
iterative	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
The	O
finite	B-Algorithm
volume	I-Algorithm
method	I-Algorithm
uses	O
this	O
criterion	O
for	O
obtaining	O
a	O
convergent	O
solution	O
and	O
implementing	O
boundary	O
conditions	O
.	O
</s>
<s>
If	O
the	O
differencing	O
scheme	O
produces	O
coefficients	O
that	O
satisfy	O
the	O
above	O
criterion	O
the	O
resulting	O
matrix	O
of	O
coefficients	O
is	O
diagonally	B-Algorithm
dominant	I-Algorithm
.	O
</s>
<s>
To	O
achieve	O
diagonal	B-Algorithm
dominance	I-Algorithm
we	O
need	O
large	O
values	O
of	O
net	O
coefficient	O
so	O
the	O
linearisation	O
practice	O
of	O
source	O
terms	O
should	O
ensure	O
that	O
SP	O
is	O
always	O
negative	O
.	O
</s>
<s>
Diagonal	B-Algorithm
dominance	I-Algorithm
is	O
a	O
desirable	O
feature	O
for	O
satisfying	O
the	O
boundedness	O
criterion	O
.	O
</s>
