The main purpose of this FORTRAN code is to compute
eigenvalues and eigenfunctions of regular and singular
Sturm-Liouville (S-L) 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 end-points 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
end-point; the latter are two coupled conditions linking the values
of solutions near the two end-points, e.g. periodic and semi-periodic
BC and their singular analogues.
SLEIGN2 can compute eigenvalues and eigenfunctions for arbitrary
self-adjoint BC, regular or singular, separated or coupled. The
singular end-points may be of limit-point or limit-circle type
and may be oscillatory or non-oscillatory. (There is one exception:
At this writing we do not have an algorithm for the case when both
endpoints are limit-point 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 S-L 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 on-line
information on data entry, end-point classifications, tolerance,
output flags, etc.
[BEWZ] P.B. Bailey, W.N. Everitt, J. Weidmann, and A. Zettl,
"Regular approximations of singular Sturm-Liouville problems",
Results in Mathematics, v.22, (1993), 3-22.
[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), 393-406.
Both [BEWZ] and [Z] are available from Home Site link given below.
Current Version: SLEIGN2
License Type: Public Domain, development partially supported by
NSF grant: DMS-9106470
Source Code Availability:
Available Binary Packages:
- Debian Package: No
- RedHat RPM Package: No
- Other Packages: No
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