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Manuscript Title: De Vogelaere's method with automatic error control.
Authors: J.P. Coleman, J. Mohamed
Program title: RADISH
Catalogue identifier: ACZB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 17(1979)283
Programming language: Fortran.
Computer: IBM 370.
Operating system: MTS.
RAM: 3K words
Word size: 32
Keywords: General purpose, De vogelaere's method, Schrodinger equation, Error control, Numerical solution, Phase shift, Second-order Differential equation.
Classification: 4.3.

Nature of problem:
The subroutine DEVOG solves any equation of the form y''=f(x,y). The test program, which provides an example of this subroutine in operation, solves the single-channel Schrodinger equation for scattering of an electron by the static potential of atomic hydrogen, for a specified energy E and angular momentum L, and calculates the scattering phase shift.

Solution method:
The differential equation is solved by de Vogelaere's method and the local truncation error is controlled by using the results of Coleman and Mohamed. To calculate the phase shift the numerical solution in the asymptotic region is expressed as a linear combination of spherical Bessel functions.

Restrictions:
The subroutine DEVOG is applicable to any linear or nonlinear equation of the form y" = f(x,y). The restriction of the test program to the static potential of hydrogen may be removed by changing the function subprogram F. The test program requires L <= 4 but restriction is easily removed.

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

Running time:
The test run which accompanies this paper took 3.4 s CPU time, in a time-sharing environment, to calculate 27 phase shifts. (A separate compilation-only run took 2.1 s.)