<s>
In	O
mathematics	O
,	O
a	O
multisymplectic	B-Algorithm
integrator	I-Algorithm
is	O
a	O
numerical	B-General_Concept
method	I-General_Concept
for	O
the	O
solution	O
of	O
a	O
certain	O
class	O
of	O
partial	O
differential	O
equations	O
,	O
that	O
are	O
said	O
to	O
be	O
multisymplectic	O
.	O
</s>
<s>
Multisymplectic	B-Algorithm
integrators	I-Algorithm
are	O
geometric	B-Algorithm
integrators	I-Algorithm
,	O
meaning	O
that	O
they	O
preserve	O
the	O
geometry	O
of	O
the	O
problems	O
;	O
in	O
particular	O
,	O
the	O
numerical	B-General_Concept
method	I-General_Concept
preserves	O
energy	O
and	O
momentum	O
in	O
some	O
sense	O
,	O
similar	O
to	O
the	O
partial	O
differential	O
equation	O
itself	O
.	O
</s>
<s>
Examples	O
of	O
multisymplectic	B-Algorithm
integrators	I-Algorithm
include	O
the	O
Euler	O
box	O
scheme	O
and	O
the	O
Preissman	O
box	O
scheme	O
.	O
</s>
<s>
where	O
is	O
the	O
unknown	O
,	O
and	O
are	O
(	O
constant	O
)	O
skew-symmetric	B-Algorithm
matrices	I-Algorithm
and	O
denotes	O
the	O
gradient	O
of	O
.	O
</s>
<s>
A	O
multisymplectic	B-Algorithm
integrator	I-Algorithm
is	O
a	O
numerical	B-General_Concept
method	I-General_Concept
for	O
solving	O
multisymplectic	O
PDEs	O
whose	O
numerical	B-General_Concept
solution	I-General_Concept
conserves	O
a	O
discrete	O
form	O
of	O
symplecticity	O
.	O
</s>
<s>
One	O
example	O
is	O
the	O
Euler	O
box	O
scheme	O
,	O
which	O
is	O
derived	O
by	O
applying	O
the	O
symplectic	B-Algorithm
Euler	I-Algorithm
method	I-Algorithm
to	O
each	O
independent	O
variable	O
.	O
</s>
<s>
Another	O
multisymplectic	B-Algorithm
integrator	I-Algorithm
is	O
the	O
Preissman	O
box	O
scheme	O
,	O
which	O
was	O
introduced	O
by	O
Preissman	O
in	O
the	O
context	O
of	O
hyperbolic	O
PDEs	O
.	O
</s>
<s>
The	O
Preissman	O
box	O
scheme	O
can	O
be	O
derived	O
by	O
applying	O
the	O
Implicit	B-Algorithm
midpoint	I-Algorithm
rule	I-Algorithm
,	O
which	O
is	O
a	O
symplectic	O
integrator	O
,	O
to	O
each	O
of	O
the	O
independent	O
variables	O
.	O
</s>
