SLEIGN
The main purpose of this FORTRAN code is to compute
eigenvalues and eigenfunctions of regular and singular
SturmLiouville (SL) problems, and to approximate the continuous
(essential) spectrum in the singular case. These problems consist of
a second order linear differential equation
(py')' + qy = lambda wy on (a,b)
together with boundary conditions (BC). The form of the BC depends
on the regular or singular classification of the endpoints a and b.
For both cases the BC fall into two major classes: separated and
coupled. The former are two separated conditions, one at each
endpoint; the latter are two coupled conditions linking the values
of solutions near the two endpoints, e.g. periodic and semiperiodic
BC and their singular analogues.
SLEIGN2 can compute eigenvalues and eigenfunctions for arbitrary
selfadjoint BC, regular or singular, separated or coupled. The
singular endpoints may be of limitpoint or limitcircle type
and may be oscillatory or nonoscillatory. (There is one exception:
At this writing we do not have an algorithm for the case when both
endpoints are limitpoint and the spectrum is unbounded above and below.)
When combined with algorithms from [BEWZ] (see reference below),
SLEIGN2 can be used to approximate the continuous spectrum of
singular SL problems, e.g. the starting point of the continuous
spectrum, gaps in the continuous spectrum, etc. For an illustration
of this method see [Z] below. An important feature of SLEIGN2 is its
user friendly, menu driven interface designed for both novice and
expert. The user need not write a computer "driver" program to call
SLEIGN2; it contains its own driver that prompts the user to enter
all necessary data about the problem from the key board. An
interactive help section is available giving the user online
information on data entry, endpoint classifications, tolerance,
output flags, etc.
[BEWZ] P.B. Bailey, W.N. Everitt, J. Weidmann, and A. Zettl,
"Regular approximations of singular SturmLiouville problems",
Results in Mathematics, v.22, (1993), 322.
[Z] A. Zettl, "Computing continuous spectrum", Proceedings of
International Symposium, "Trends and developments in ordinary
differential equations", edited by Y. Alavi and P.F. Hsieh, World
Scientific, (1997), 393406.
Both [BEWZ] and [Z] are available from Home Site link given below.
