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PROGRAM LIBRARY JINRLIBSLIPM - a MAPLE Package for Numerical Solution
of Sturm-Liouville Partial Problems |
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Environment: MAPLE/Windows 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 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 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 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
SLIPM_USER SUPPLIED PROCEDURES_LegendreEquation.mw and
for calculating the solutions to the Legendre and Whittaker equations,
correspondingly, are presented too.
SLIPM_USER SUPPLIED PROCEDURES_WhittakerEquation.mw References:
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, 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.
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.
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.
is presented.
The two sets of the user procedures:
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