SLIP1 |
- |
the numerical solution of the Sturm-Liouville
problem basing on the continuous analog of the Newton method; |

SLIPS2 |
- |
numerical solution of the Sturm-Liouville problem
for the system of differential equations; |

SLIPH4 |
- |
numerical solution of the Sturm-Liouville problem. |

SLIP1 - PROGRAM OF THE NUMERICAL SOLUTION OF THE STURM-LIOUVILLE PROBLEM

BASING ON THE CONTINUOUS ANALOG OF THE NEWTON METHOD

Authors: I.V.Puzynin, T.P.Puzynina

Language: Fortran

The algorithm of the numerical solution of the Sturm-Liouville
problem was described basing on the continuous analog of the
Newton method. The program was described realizing this
algorithm on Fortran too.

Sources and the detailed description (in Russian, format .ps) are submitted.

SLIPS2 - PROGRAM COMLEX FOR NUMERICAL SOLUTION OF THE STURM-LIOUVILLE PROBLEM

FOR THE SYSTEM OF DIFFERENTIAL EQUATIONS

Author: T.P.Puzynina

Language: Fortran

A program complex SLIPS2 is intended for solving a partial Sturm-Liouville
problem for a system of two 2-nd order differential equations with
predetermined boundary conditions.
The software realizes modified iteration schemes of the continuous analogue
of Newton's method with selection of an iteration parameter.
Among them there is a scheme with a fixed eigenvalue shift and
orthogonalization of the eigenfunction vector at each iteration.

The program was used for calculation of energy levels and wave functions
of mesomolecules and a scattering problem in a two-level approximation of
an adiabatic representation of a three-body problem with Coulomb interation
as well as for the inverse scattering problem in the framework of Bargmann
formalism and for a number of other problems.

The program can be effectively used on its own and as a generator of initial
approximations at numerical analysis of convergence of various multi-level
approximations for quantum mechanics systems.

The text of the program is written in the Fortran language and an example
of its use is presented.

Sources and the detailed description (in Russian, format .ps) are submitted.

SLIPH4 - PROGRAM COMLEX FOR NUMERICAL SOLUTION OF THE STURM-LIOUVILLE PROBLEM

Authors: I.V.Puzynin, T.P.Puzynina, T.A.Strizh

Language: Fortran

SLIPH4 program complex for the numerical solution of the Sturm-
Liouville problem for the second-order homogeneous linear differential
equation with homogeneous boundary conditions is described.

The continuous analogue of the Newton method is used. The descrete
scheme that has been realized in the approach provides an accuracy
of the order of four with respect to the mesh step of the independent
variable. The program for the initial approximation to the solution
calculations with the help of a modified Newton method for the
polynomial roots finding with the calculated root elimination is
added to the complex. The possibility of using the modified method
with eigenvalue fixing and obtained approximate eigenfunction
additional orthogonalizaton is realized in complex. This permits to
solve both the initial approximation problem and its more precise
definition by the same scheme.

The program write-up is presented.
Examples illustrating the program complex using are given.

The investigation has been performed at the Laboratory of Computing
Techniques and Automation, JINR.

Sources and the detailed description (in Russian, format .ps) are submitted.