## 3. Numerical procedure and boundary conditionsWe solve Eq. (13) numerically subject to boundary conditions at the centre of the
sheet, so that one has control over the parity of the solution (kink
or sausage). At
we take
to be zero; the integration range is therefore
. Lengths and speeds are normalised against the
half-width such that The boundary conditions at
for the kink mode are given by
,
; for the sausage mode,
and
at
. The constant To obtain a solution of the Eq. (13) we use a fixed value of
and integrate the two first order equations
(22) using the NAG routine D02BEF. The integration is performed
between
, where proper initial conditions for
and
are available, and
, where the condition
must be satisfied. A Newton iteration, with NAG
routine C05AXF, is done by changing
and integrating from
to
until the boundary condition at the second
point is satisfied. The value of
is chosen to be large, typically
, except for short wavelengths where it was
found that a smaller
(e.g. 10 © European Southern Observatory (ESO) 1997 Online publication: April 8, 1998 |