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The method of raptis and allison with automatic error control
C-638 Computer Physics Communications 20 (1980) 309-320 © North-Holland Publishing Company
THE M E T H O D O F R A P T I S A N D A L L I S O N WITH A U T O M A T I C E R R O R C O N T R O L Julie M O H A M E D *
Department of Mathematics, University o f Durham, Durham, UK Received 14 September 1979
PROGRAM SUMMARY
Title of program: EXPFIT1 Catalogue number: AANA Computer: IBM 370;Installation: NUMAC (Northumbrian Universities Multiple Access Computer)
Operating system: MTS Programming language: FORTRAN IV High speed storage required: 3675 words Number o f bits in a word: 32 Overlay structure: none Number of magnetic tapes: none Other peripherals: card reader, line printer Number o f cards in combined program and test deck: 763 Keywords: the method of Raptis and Allison, SchriSdinger equation, classical turning point, numerical solution, second order differential equation, error control, phase shifts
Method o f calculation The differential equation is solved by the method of Raptis and Allison 11 ] and the local truncation error is controlled as in Mohamed [2]. To calculate the phase shift the numerical solution in the asymptotic region is expressed as a linear combination of spherical Bessel functions.
Restrictions on the complexity of the problem 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.
Running time Nature of the physical problem Program EXPF1T 1 solves the single channel radial Schrbdinger equation in the form
_(L(L + 1) y " ( x ) - [ x~
E+ V(x)ly(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.
The test run which accompanies this paper took 4.8 s CPU time in a time-sharing environment; a separate compilationonly run took 3.3 s.
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.
References 11] J. Mohamed, Ph.D. Thesis, University of Durham (1979). 12] A. Raptis and A.C. Allison, Comput. Phys. Commun. 14 (1978) 1.
* Present address: University of Liverpool, Department of Computational and Statistical Science, Brownlow Hill, Liverpool L69 3BX, UK.
THE M E T H O D O F R A P T I S A N D A L L I S O N WITH A U T O M A T I C E R R O R C O N T R O L Julie M O H A M E D *
Department of Mathematics, University o f Durham, Durham, UK Received 14 September 1979
PROGRAM SUMMARY
Title of program: EXPFIT1 Catalogue number: AANA Computer: IBM 370;Installation: NUMAC (Northumbrian Universities Multiple Access Computer)
Operating system: MTS Programming language: FORTRAN IV High speed storage required: 3675 words Number o f bits in a word: 32 Overlay structure: none Number of magnetic tapes: none Other peripherals: card reader, line printer Number o f cards in combined program and test deck: 763 Keywords: the method of Raptis and Allison, SchriSdinger equation, classical turning point, numerical solution, second order differential equation, error control, phase shifts
Method o f calculation The differential equation is solved by the method of Raptis and Allison 11 ] and the local truncation error is controlled as in Mohamed [2]. To calculate the phase shift the numerical solution in the asymptotic region is expressed as a linear combination of spherical Bessel functions.
Restrictions on the complexity of the problem 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.
Running time Nature of the physical problem Program EXPF1T 1 solves the single channel radial Schrbdinger equation in the form
_(L(L + 1) y " ( x ) - [ x~
E+ V(x)ly(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.
The test run which accompanies this paper took 4.8 s CPU time in a time-sharing environment; a separate compilationonly run took 3.3 s.
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.
References 11] J. Mohamed, Ph.D. Thesis, University of Durham (1979). 12] A. Raptis and A.C. Allison, Comput. Phys. Commun. 14 (1978) 1.
* Present address: University of Liverpool, Department of Computational and Statistical Science, Brownlow Hill, Liverpool L69 3BX, UK.