<s>
Numerov	B-Algorithm
's	I-Algorithm
method	I-Algorithm
(	O
also	O
called	O
Cowell	B-Algorithm
's	I-Algorithm
method	I-Algorithm
)	O
is	O
a	O
numerical	B-Algorithm
method	I-Algorithm
to	O
solve	O
ordinary	O
differential	O
equations	O
of	O
second	O
order	O
in	O
which	O
the	O
first-order	O
term	O
does	O
not	O
appear	O
.	O
</s>
<s>
It	O
is	O
a	O
fourth-order	O
linear	B-Algorithm
multistep	I-Algorithm
method	I-Algorithm
.	O
</s>
<s>
Numerov	B-Algorithm
's	I-Algorithm
method	I-Algorithm
was	O
developed	O
by	O
the	O
Russian	O
astronomer	O
Boris	O
Vasil'evich	O
Numerov	O
.	O
</s>
<s>
This	O
is	O
an	O
implicit	O
linear	B-Algorithm
multistep	I-Algorithm
method	I-Algorithm
,	O
which	O
reduces	O
to	O
the	O
explicit	O
method	O
given	O
above	O
if	O
is	O
linear	O
in	O
by	O
setting	O
.	O
</s>
<s>
This	O
equation	O
can	O
be	O
reduced	O
to	O
the	O
form	O
necessary	O
for	O
the	O
application	O
of	O
Numerov	B-Algorithm
's	I-Algorithm
method	I-Algorithm
with	O
the	O
following	O
substitution	O
:	O
</s>
<s>
We	O
can	O
rewrite	O
the	O
equation	O
a	O
little	O
bit	O
differently	O
and	O
thus	O
see	O
the	O
possible	O
application	O
of	O
Numerov	B-Algorithm
's	I-Algorithm
method	I-Algorithm
more	O
clearly	O
:	O
</s>
<s>
To	O
derive	O
the	O
Numerov	B-Algorithm
's	I-Algorithm
method	I-Algorithm
for	O
solving	O
this	O
equation	O
,	O
we	O
begin	O
with	O
the	O
Taylor	O
expansion	O
of	O
the	O
function	O
we	O
want	O
to	O
solve	O
,	O
,	O
around	O
the	O
point	O
:	O
</s>
<s>
This	O
yields	O
the	O
Numerov	B-Algorithm
's	I-Algorithm
method	I-Algorithm
if	O
we	O
ignore	O
the	O
term	O
of	O
order	O
.	O
</s>
