<s>
In	O
the	O
area	O
of	O
mathematics	O
known	O
as	O
numerical	B-Algorithm
ordinary	I-Algorithm
differential	I-Algorithm
equations	I-Algorithm
,	O
the	O
direct	B-Algorithm
multiple	I-Algorithm
shooting	I-Algorithm
method	I-Algorithm
is	O
a	O
numerical	B-Algorithm
method	I-Algorithm
for	O
the	O
solution	O
of	O
boundary	O
value	O
problems	O
.	O
</s>
<s>
The	O
method	O
constitutes	O
a	O
significant	O
improvement	O
in	O
distribution	O
of	O
nonlinearity	O
and	O
numerical	B-Algorithm
stability	I-Algorithm
over	O
single	O
shooting	B-Algorithm
methods	I-Algorithm
.	O
</s>
<s>
Single	O
shooting	B-Algorithm
methods	I-Algorithm
proceed	O
as	O
follows	O
.	O
</s>
<s>
The	O
multiple	O
shooting	B-Algorithm
method	I-Algorithm
solves	O
the	O
boundary	O
value	O
problem	O
by	O
solving	O
this	O
system	O
of	O
equations	O
.	O
</s>
<s>
Multiple	O
shooting	O
has	O
been	O
adopted	O
to	O
derive	O
parallel	B-Operating_System
solvers	O
for	O
initial	O
value	O
problems	O
.	O
</s>
<s>
For	O
example	O
,	O
the	O
Parareal	B-Operating_System
parallel-in-time	O
integration	O
method	O
can	O
be	O
derived	O
as	O
a	O
multiple	O
shooting	O
algorithm	O
with	O
a	O
special	O
approximation	O
of	O
the	O
Jacobian	O
.	O
</s>
