Icon 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

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