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De vogelaere's method with automatic error control
C-554 Computer Physics Communications 17 (1979) 283-300 © North-Holland Publishing Company
DE V O G E L A E R E ' S M E T H O D WITH A U T O M A T I C E R R O R C O N T R O L J o h n P. C O L E M A N and Julie M O H A M E D
Department o f Mathematics, University of Durham, South Road, Durham, UK Received 18 August 1978
PROGRAM SUMMARY
Title of program: RADISH Catalogue number: ACZB Computer: IBM 370; Installation: NUMAC (Northumbrian
y" = f(x, y). The test program, which provides an example of this subroutine in operation, solves the single-channel Schri~dinger 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.
Universities Multiple Access Computer)
Method o f calculation Operating system: MTS
High speed storage required: 2686 words (DEVOG 1043)
The differential equation is solved by de Vogelaere's method [1] and the local truncation error is controlled by using the results of Coleman and Mohamed [2]. To calculate the phase shift the numerical solution in the asymptotic region is expressed as a linear combination of spherical Bessel functions.
Number o f bits in a word: 32
Restrictions on the complexity o f the problem
Programming language: FORTRAN IV
Other peripherals: card reader, line printer
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 this restriction is easily removed (see section 5.1).
Number o f cards in combined program and test deck: 604
Running time
Keywords: general purpose, de Vogelaere's method, Schr6-
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.)
Overlay structure: none Number o f magnetic tapes: none
dinger equation, error control, numerical solution, phase shifts, second-order differential equation, integration
Nature o f the physical problem The subroutine DEVOG solves any equation of the form
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.
References [1] R. de Vogelaere, J. Res. Nat. Bur. Std. B 54 (1955) 119. [2] J.P. Coleman and J. Mohamed, Math. Comput. 32 (1978) 751.
DE V O G E L A E R E ' S M E T H O D WITH A U T O M A T I C E R R O R C O N T R O L J o h n P. C O L E M A N and Julie M O H A M E D
Department o f Mathematics, University of Durham, South Road, Durham, UK Received 18 August 1978
PROGRAM SUMMARY
Title of program: RADISH Catalogue number: ACZB Computer: IBM 370; Installation: NUMAC (Northumbrian
y" = f(x, y). The test program, which provides an example of this subroutine in operation, solves the single-channel Schri~dinger 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.
Universities Multiple Access Computer)
Method o f calculation Operating system: MTS
High speed storage required: 2686 words (DEVOG 1043)
The differential equation is solved by de Vogelaere's method [1] and the local truncation error is controlled by using the results of Coleman and Mohamed [2]. To calculate the phase shift the numerical solution in the asymptotic region is expressed as a linear combination of spherical Bessel functions.
Number o f bits in a word: 32
Restrictions on the complexity o f the problem
Programming language: FORTRAN IV
Other peripherals: card reader, line printer
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 this restriction is easily removed (see section 5.1).
Number o f cards in combined program and test deck: 604
Running time
Keywords: general purpose, de Vogelaere's method, Schr6-
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.)
Overlay structure: none Number o f magnetic tapes: none
dinger equation, error control, numerical solution, phase shifts, second-order differential equation, integration
Nature o f the physical problem The subroutine DEVOG solves any equation of the form
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.
References [1] R. de Vogelaere, J. Res. Nat. Bur. Std. B 54 (1955) 119. [2] J.P. Coleman and J. Mohamed, Math. Comput. 32 (1978) 751.