SLIPM                    Library "JINRLIB"                       
 
    Authors: I.V.Puzynin, T.P.Puzynina, V.T.Thach                    You are
    Environment: MAPLE/Windows                                       
                                                                     visitor here.

               SLIPM - a MAPLE Package for Numerical Solution 
                    of Sturm-Liouville Partial Problems
              Based on the Continuous Analog of Newton's Method 
        
    SLIPM (Sturm - LIouville Problem in MAPLE) is a software complex written in 
    the language of the computer algebra system MAPLE, consisting of the main 
    program SLIPM.mw and of some procedures. It is intended for a numerical solution 
    with the help of the continuous analog of Newton's method (CANM) [1,2] of 
    Sturm-Liouville partial problems, i.e., for calculating some eigenvalue of linear
    second-order differential operator and a corresponding eigenfunction satisfying 
    homogeneous boundary conditions of general type.

    SLIPM is the development of the written in the Fortran language software 
    complexes SLIP1 [3] and SLIPH4 [4]: it is added by two new ways of calculating 
    the initial value of iterative parameter , by a procedure for calculating 
    a higher precision solution (eigenvalue and corresponding eigenfunction) with 
    the help of Richardson's extrapolation method, by graphical visualization 
    procedures of intermediate and final results of the iterative process and 
    by saving of the results on a disk file.

    In the works [5,6] the description of a mathematical formulation of this problem,
    of a method CANM for its solution are given. The used newtonian schemes and 
    algorithms for the calculating the iterative parameter  are 
    described. The examples of using the package SLIPM for the calculating the 
    solutions of Schredinger equation with the Morse potential for mesomolecule , 
    of Legendre and Whittaker equations are described.

    In the work [7] descriptions of the procedures of the software complex and 
    their parameters are given. The question concerning the calculating precision 
    of power  for realized discrete schemes is researched. The process of 
    increasing the precision of results to power  by using procedure RICHARD, 
    which realizes the extrapolation Richardson's method on the set of three twice 
    condensed nets, is described.

    The source of package SLIPM_MORSE.mw, input data files RICHARDSON1.txt, 
    RICHARDSON2.txt, RICHARDSON4.txt and output files SLIPM.txt, SLIPMOH4.txt with
    results are presented in archive.
    In applied test the example for calculating a nodeless solution of Schredinger 
    equation with the Morse potential for mesomolecule  is presented.
    The two sets of the user procedures
    SLIPM_USER SUPPLIED PROCEDURES_LegendreEquation.mw  and 
    SLIPM_USER SUPPLIED PROCEDURES_WhittakerEquation.mw 
    for calculating the solutions to the Legendre and Whittaker equations, 
    correspondingly, are presented too.

    References:
    -----------
    1. I.V. Puzynin, et al. General Continue Analog of the Newton's Method for 
       Numerical Research of some Quantum-Field Models. Physics of Elementary 
       Particles and Atomic Nuclei, 1999, V.30, No.1, P.87-110.
    2. I.V. Puzynin, et al. Methods of Computational Physics for Investigation  
       of Models of Complex Physical Systems. Physics of Elementary Particles and 
       Atomic Nuclei, 2007, V.38, No.1, P.70-116.
    3. I.V. Puzynin, T.P. Puzynina. SLIP1 - Program for the numerical solution of 
       the Sturm-Liouville problem basing on the continuous analog of the Newton 
       method. Collection of scientific papers in collaboration of JINR, Dubna, 
       USSR and Central Research Institute for Physics, Budapest, Hungary, KFKI-74-34,
       1974, pp.93-112.
       http://www.jinr.ru/programs/jinrlib/slip/indexe.html 
    4. I.V. Puzynin, T.P. Puzynina, T.A. Strizh. SLIPH4 - Program for numerical 
       solution of the Sturm-Liouville problem. JINR Report, P11-87-332, Dubna, 1987.
       http://www.jinr.ru/programs/jinrlib/slip/indexe.html 
    5. И.В.Пузынин, Т.П. Пузынина, Во Чонг Тхак. SLIPM - программа на языке MAPLE для
       численного решения частичной проблемы Штурма-Лиувилля на основе непрерывного
       аналога метода Ньютона. Вестник РУДН, серия "Математика. Информатика. Физика"
       No.2 вып.2,2010,С.89-97.
    6. SLIPM - программа на языке MAPLE для численного решения частичной проблемы
       Штурма-Лиувилля на основе непрерывного аналога метода Ньютона. 
       I. Алгоритм. Препринт ОИЯИ Р11-2010-2, Дубна, 2010, С.9.
    7. SLIPM - программа на языке MAPLE для численного решения частичной проблемы
       Штурма-Лиувилля на основе непрерывного аналога метода Ньютона. 
       II. Программная реализация. Препринт ОИЯИ Р11-2010-95, Дубна, 2010, С.8.