<s>
The	O
Newmark-beta	B-Algorithm
method	I-Algorithm
is	O
a	O
method	B-Algorithm
of	O
numerical	B-Algorithm
integration	I-Algorithm
used	O
to	O
solve	O
certain	O
differential	O
equations	O
.	O
</s>
<s>
The	O
method	B-Algorithm
is	O
named	O
after	O
Nathan	O
M	O
.	O
Newmark	O
,	O
former	O
Professor	O
of	O
Civil	O
Engineering	O
at	O
the	O
University	O
of	O
Illinois	O
at	O
Urbana	O
–	O
Champaign	O
,	O
who	O
developed	O
it	O
in	O
1959	O
for	O
use	O
in	O
structural	B-Algorithm
dynamics	I-Algorithm
.	O
</s>
<s>
Using	O
the	O
extended	O
mean	O
value	O
theorem	O
,	O
the	O
Newmark	O
-	O
method	B-Algorithm
states	O
that	O
the	O
first	O
time	O
derivative	O
(	O
velocity	O
in	O
the	O
equation	O
of	O
motion	O
)	O
can	O
be	O
solved	O
as	O
,	O
</s>
