<s>
In	O
numerical	B-General_Concept
analysis	I-General_Concept
,	O
the	O
split-step	O
(	O
Fourier	O
)	O
method	O
is	O
a	O
pseudo-spectral	B-Algorithm
numerical	O
method	O
used	O
to	O
solve	O
nonlinear	O
partial	O
differential	O
equations	O
like	O
the	O
nonlinear	O
Schrödinger	O
equation	O
.	O
</s>
<s>
Second	O
,	O
it	O
is	O
necessary	O
to	O
Fourier	B-Algorithm
transform	I-Algorithm
back	O
and	O
forth	O
because	O
the	O
linear	O
step	O
is	O
made	O
in	O
the	O
frequency	O
domain	O
while	O
the	O
nonlinear	O
step	O
is	O
made	O
in	O
the	O
time	O
domain	O
.	O
</s>
<s>
However	O
,	O
the	O
split-step	B-Algorithm
method	I-Algorithm
provides	O
a	O
numerical	B-General_Concept
solution	I-General_Concept
to	O
the	O
problem	O
.	O
</s>
<s>
Another	O
application	O
of	O
the	O
split-step	B-Algorithm
method	I-Algorithm
that	O
has	O
been	O
gaining	O
a	O
lot	O
of	O
traction	O
since	O
the	O
2010s	O
is	O
the	O
simulation	O
of	O
Kerr	O
frequency	O
comb	O
dynamics	O
in	O
optical	O
microresonators	O
.	O
</s>
<s>
By	O
taking	O
the	O
inverse	O
Fourier	B-Algorithm
transform	I-Algorithm
of	O
one	O
obtains	O
;	O
the	O
pulse	O
has	O
thus	O
been	O
propagated	O
a	O
small	O
step	O
.	O
</s>
<s>
wave	O
numbers	O
)	O
associated	O
with	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
of	O
whatever	O
is	O
being	O
operated	O
on	O
.	O
</s>
<s>
where	O
denotes	O
a	O
Fourier	B-Algorithm
transform	I-Algorithm
.	O
</s>
<s>
A	O
variation	O
on	O
this	O
method	O
is	O
the	O
symmetrized	O
split-step	B-Algorithm
Fourier	I-Algorithm
method	I-Algorithm
,	O
which	O
takes	O
half	O
a	O
time	O
step	O
using	O
one	O
operator	O
,	O
then	O
takes	O
a	O
full-time	O
step	O
with	O
only	O
the	O
other	O
,	O
and	O
then	O
takes	O
a	O
second	O
half	O
time	O
step	O
again	O
with	O
only	O
the	O
first	O
.	O
</s>
<s>
This	O
method	O
is	O
an	O
improvement	O
upon	O
the	O
generic	O
split-step	B-Algorithm
Fourier	I-Algorithm
method	I-Algorithm
because	O
its	O
error	O
is	O
of	O
order	O
for	O
a	O
time	O
step	O
.	O
</s>
<s>
The	O
Fourier	B-Algorithm
transforms	I-Algorithm
of	O
this	O
algorithm	O
can	O
be	O
computed	O
relatively	O
fast	O
using	O
the	O
fast	O
Fourier	B-Algorithm
transform	I-Algorithm
(	O
FFT	O
)	O
.	O
</s>
<s>
The	O
split-step	B-Algorithm
Fourier	I-Algorithm
method	I-Algorithm
can	O
therefore	O
be	O
much	O
faster	O
than	O
typical	O
finite	B-Algorithm
difference	I-Algorithm
methods	I-Algorithm
.	O
</s>
