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Manuscript Title: The method of Raptis and Allison with automatic error control.
Authors: J. Mohamed
Program title: EXPFIT1
Catalogue identifier: AANA_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 20(1980)309
Programming language: Fortran.
Computer: IBM 370.
Operating system: MTS.
RAM: 4K words
Word size: 32
Keywords: General purpose, The method of raptis And allison, Schrodinger equation, Classical turning point, Numerical solution, Second order Differential equation, Error control, Phase shifts.
Classification: 4.3.

Nature of problem:
Program EXPFIT1 solves the single channel radial Schrodinger equation in the form y''(x) = (L*(L+1)/x**2 - E + V(x)) * y(x). The test program solves the above problem for scattering of an electron by the static potential of atomic hydrogen, for a range of values of the energy E and angular momentum L. The solution is calculated to a specified accuracy; scattering phase shifts are also calculated.

Solution method:
The differential equation is solved by the method of Raptis and Allision and the local truncation error is controlled as in Mohamed. To calculate the phase shift the numerical solution in the asymptotic region is expressed as a linear combination of spherical Bessel functions.

The restriction of the test program to the static potential of hydrogen may easily be removed by changing the function subprogram POT. The arrays F, XX which store the values of the solution and the corresponding mesh points may each store up to 8000 elements; the range of integration (which is specified by the user) and the values of the steplength chosen automatically by RAPAL may be such as to necessitate larger F and XX arrays but this can be easily arranged.

Unusual features:
The steplengths used in solving the differential equation are chosen automatically by the program, in routine RAPAL, in accordance with a local accuracy criterion supplied by the user.

Running time:
The test run which accompanies this paper took 4.8 s CPU time in a time- sharing environment; a separate compilation only took 3.3 s.