MATSLISE: a software package for the numerical solution of Sturm-Liouville and Schrödinger problems

paper to reference: V. LEDOUX, M. VAN DAELE and G. VANDEN BERGHE, Matslise: A Matlab package for the Numerical Solution of Sturm-Liouville and Schrödinger equations, ACM Transactions on Mathematical Software, 31 (2005), 532-554.

MATSLISE is a graphical Matlab software package for the numerical study of regular Sturm-Liouville problems, one-dimensional Schrödinger equations and radial Schrödinger equations with a distorted coulomb potential. It allows the fast and accurate computation of the eigenvalues and the visualization of the corresponding eigenfunctions. This is realized by making use of the power of high order CP methods (abbreviation for Constant reference potential Perturbation Method). The CP methods exhibit the advantage that with them the energy dependence of the error is bounded: very accurate results at high values of the eigenvalue-index are reached in a considerably small time span.

Given the interest of researches in various fields, a graphical user interface (GUI) has been developed. The GUI allows to enter the input in a straightforward manner, to control certain parameters interactively and to present the results graphically.

Downloading the software

Feb. 2007:	Download latest MATSLISE-version. For any problems or comments, please email to Veerle.Ledoux[AT]UGent.be.
May. 2008:	The current MATSLISE package is designed for well-behaved coefficient functions which are continuous over the integration interval. Using MATSLISE with discontinuities in the potential or in one of the coefficient functions of a Sturm-Liouville gives results which can not be trusted. However the CP-methods can deal with discontinuities by simply including these discontinuities as meshpoints in the constructed mesh. The MATSLISE_PC package allows the solution of Schrodinger problems with a potential function which is continuous except for finitely many jumps. The user has to specify the location of the jumps and these jumps are then added to the mesh. Download MATSLISE_PC (no GUI-version available).
Dec. 2008:	A new version of MATSLISE is available which does not require the MATLAB symbolic toolbox. Automatic differentiation is used in the Liouville transformation.
UPDATE	Matslise and related software has moved to http://www.nummath.ugent.be/SLsoftware

Requirements

MATSLISE uses the Matlab symbolic toolbox.

Disclaimer

MATSLISE is freely available for academic or non-profit use. In no circumstances can the authors be held responsible for any deficiency, fault or other mishappening with regard to the use or performance of MATSLISE.

Contact

Veerle.Ledoux@UGent.be
Department of Applied Mathematics & Computer Science
Krijgslaan 281 - S9
B-9000 GENT
Belgium

References

V. LEDOUX, M. VAN DAELE and G. VANDEN BERGHE, Matslise: A Matlab package for the Numerical Solution of Sturm-Liouville and Schrödinger equations, ACM Transactions on Mathematical Software, 31 (2005), 532-554.
L. GR. IXARU, Numerical Methods for Differential Equations and Applications. Reidel, Dordrecht-Boston-Lancaster, 1984.
L. GR. IXARU, CP methods for the Schrodinger equation, J. Comput. Appl. Math., 125 (2000), 347-357.
L. GR. IXARU, H. DE MEYER and G. VANDEN BERGHE, Highly accurate eigenvalues for the distorted Coulomb potential, Phys. Rev. E, 61 (2000), 3151-3159.
V. LEDOUX, M. VAN DAELE and G. VANDEN BERGHE, CP methods of higher order for Sturm-Liouville and Schrödinger equations, Comp. Phys. Commun., 162 (2004), 151-165.