<s>
Explicit	O
formulas	O
for	O
eigenvalues	B-Algorithm
and	I-Algorithm
eigenvectors	I-Algorithm
of	I-Algorithm
the	I-Algorithm
second	I-Algorithm
derivative	I-Algorithm
with	O
different	O
boundary	O
conditions	O
are	O
provided	O
both	O
for	O
the	O
continuous	O
and	O
discrete	O
cases	O
.	O
</s>
<s>
In	O
the	O
discrete	O
case	O
,	O
the	O
standard	O
central	O
difference	O
approximation	O
of	O
the	O
second	B-Algorithm
derivative	I-Algorithm
is	O
used	O
on	O
a	O
uniform	O
grid	O
.	O
</s>
<s>
These	O
formulas	O
are	O
used	O
to	O
derive	O
the	O
expressions	O
for	O
eigenfunctions	B-Algorithm
of	O
Laplacian	O
in	O
case	O
of	O
separation	O
of	O
variables	O
,	O
as	O
well	O
as	O
to	O
find	O
eigenvalues	O
and	O
eigenvectors	O
of	O
multidimensional	O
discrete	B-Algorithm
Laplacian	I-Algorithm
on	O
a	O
regular	O
grid	O
,	O
which	O
is	O
presented	O
as	O
a	O
Kronecker	B-Algorithm
sum	I-Algorithm
of	I-Algorithm
discrete	I-Algorithm
Laplacians	I-Algorithm
in	O
one-dimension	O
.	O
</s>
