<s>
High-order	O
compact	O
finite	B-Algorithm
difference	I-Algorithm
schemes	I-Algorithm
are	O
used	O
for	O
solving	O
third-order	O
differential	O
equations	O
created	O
during	O
the	O
study	O
of	O
obstacle	O
boundary	O
value	O
problems	O
.	O
</s>
<s>
The	O
convergence	B-Architecture
rate	I-Architecture
of	O
the	O
high-order	O
compact	O
scheme	O
is	O
third	O
order	O
,	O
the	O
second-order	O
scheme	O
is	O
fourth	O
order	O
.	O
</s>
<s>
Finite	B-Algorithm
difference	I-Algorithm
methods	I-Algorithm
are	O
amongst	O
the	O
most	O
popular	O
methods	O
that	O
have	O
been	O
applied	O
most	O
frequently	O
in	O
solving	O
such	O
differential	O
equations	O
.	O
</s>
<s>
A	O
finite	B-Algorithm
difference	I-Algorithm
scheme	I-Algorithm
is	O
compact	O
in	O
the	O
sense	O
that	O
the	O
discretised	O
formula	O
comprises	O
at	O
most	O
nine	O
point	O
stencils	B-Algorithm
which	O
includes	O
a	O
node	O
in	O
the	O
middle	O
about	O
which	O
differences	O
are	O
taken	O
.	O
</s>
<s>
In	O
addition	O
,	O
greater	O
order	O
of	O
accuracy	O
(	O
more	O
than	O
two	O
)	O
justifies	O
the	O
terminology	O
'	O
higher-order	B-Algorithm
compact	I-Algorithm
finite	I-Algorithm
difference	I-Algorithm
scheme	I-Algorithm
 '	O
(	O
HOC	O
)	O
.	O
</s>
<s>
The	O
higher-order	O
compact	O
scheme	O
considered	O
here	O
is	O
by	O
using	O
the	O
original	O
differential	O
equation	O
to	O
substitute	O
for	O
the	O
leading	O
truncation	B-Algorithm
error	I-Algorithm
terms	O
in	O
the	O
finite	O
difference	O
equation	O
.	O
</s>
