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Volumn 158, Issue 1, 2003, Pages 93-106

A generator of hybrid symmetric four-step methods for the numerical solution of the Schrödinger equation

Author keywords

Algebraic order; Explicit methods; Hybrid methods; Initial value problems; Interval of periodicity; Phase lag; Schr dinger equation

Indexed keywords

ALGEBRA; NUMERICAL METHODS; PHASE MEASUREMENT;

EID: 0042785945     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(03)00469-2     Document Type: Article
Times cited : (154)

References (28)
  • 1
    • 0001401038 scopus 로고
    • The numerical solution of coupled differential equations arising from the Schrödinger equation
    • Allison A.C. The numerical solution of coupled differential equations arising from the Schrödinger equation J. Comput. Phys. 6 1970 378-391
    • (1970) J. Comput. Phys. , vol.6 , pp. 378-391
    • Allison, A.C.1
  • 2
    • 0035341433 scopus 로고    scopus 로고
    • A generator of hybrid explicit methods for the numerical solution of the Schrödinger equation and related problems
    • Avdelas G. Konguetsof A. Simos T.E. A generator of hybrid explicit methods for the numerical solution of the Schrödinger equation and related problems Comput. Phys. Comm. 136 2001 14-28
    • (2001) Comput. Phys. Comm. , vol.136 , pp. 14-28
    • Avdelas, G.1    Konguetsof, A.2    Simos, T.E.3
  • 3
    • 0002207932 scopus 로고    scopus 로고
    • Embedded methods for the numerical solution of the Schrödinger equation
    • Avdelas G. Simos T.E. Embedded methods for the numerical solution of the Schrödinger equation Comput. Math. Appl. 31 1996 85-102
    • (1996) Comput. Math. Appl. , vol.31 , pp. 85-102
    • Avdelas, G.1    Simos, T.E.2
  • 4
    • 0033114512 scopus 로고    scopus 로고
    • Embedded eighth order methods for the numerical solution of the Schrödinger equation
    • Avdelas G. Simos T.E. Embedded eighth order methods for the numerical solution of the Schrödinger equation J. Math. Chem. 25 1999 327-341
    • (1999) J. Math. Chem. , vol.25 , pp. 327-341
    • Avdelas, G.1    Simos, T.E.2
  • 5
    • 0019010803 scopus 로고
    • A one-step method for direct integration of structural dynamic equations
    • Brusa L. Nigro L. A one-step method for direct integration of structural dynamic equations Internat. J. Numer. Methods Engrg. 15 1980 685-699
    • (1980) Internat. J. Numer. Methods Engrg. , vol.15 , pp. 685-699
    • Brusa, L.1    Nigro, L.2
  • 6
    • 0021578695 scopus 로고
    • A Numerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
    • Chawla M.M. Rao P.S. A Numerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems J. Comput. Appl. Math. 11 1984 277-281
    • (1984) J. Comput. Appl. Math. , vol.11 , pp. 277-281
    • Chawla, M.M.1    Rao, P.S.2
  • 7
    • 0022752603 scopus 로고
    • Numerov-type method with minimal phase-lag for the integration of second order periodic initial-value problem. II. Explicit method
    • Chawla M.M. Rao P.S. Numerov-type method with minimal phase-lag for the integration of second order periodic initial-value problem. II. Explicit method J. Comput. Appl. Math. 15 1986 329-337
    • (1986) J. Comput. Appl. Math. , vol.15 , pp. 329-337
    • Chawla, M.M.1    Rao, P.S.2
  • 8
    • 0023315288 scopus 로고
    • An explicit sixth-order method with phase-lag of order eight for y″=f(t,y)
    • Chawla M.M. Rao P.S. An explicit sixth-order method with phase-lag of order eight for y″=f(t,y) J. Comput. Appl. Math. 16 1987 365-368
    • (1987) J. Comput. Appl. Math. , vol.16 , pp. 365-368
    • Chawla, M.M.1    Rao, P.S.2
  • 9
    • 0001330331 scopus 로고
    • Numerical methods for y″=f(x,y) via rational approximation for the cosine
    • Coleman J.P. Numerical methods for y″=f(x,y) via rational approximation for the cosine IMA J. Numer. Anal. 9 1989 145-165
    • (1989) IMA J. Numer. Anal. , vol.9 , pp. 145-165
    • Coleman, J.P.1
  • 12
    • 77958409581 scopus 로고
    • Symmetric multistep methods for periodic initial value problems
    • Lambert J.D. Watson I.A. Symmetric multistep methods for periodic initial value problems J. Inst. Math. Appl. 18 1976 189-202
    • (1976) J. Inst. Math. Appl. , vol.18 , pp. 189-202
    • Lambert, J.D.1    Watson, I.A.2
  • 15
    • 0001752844 scopus 로고
    • A variable step method for the numerical integration of the one-dimensional Schrödinger equation
    • Raptis A.D. Cash J.R. A variable step method for the numerical integration of the one-dimensional Schrödinger equation Comput. Phys. Comm. 36 1985 113-119
    • (1985) Comput. Phys. Comm. , vol.36 , pp. 113-119
    • Raptis, A.D.1    Cash, J.R.2
  • 16
    • 0001591709 scopus 로고
    • New variable-step procedure for the numerical integration of the one-dimensional Schrödinger equation
    • Simos T.E. New variable-step procedure for the numerical integration of the one-dimensional Schrödinger equation J. Comput. Phys. 108 1993 175
    • (1993) J. Comput. Phys. , vol.108 , pp. 175
    • Simos, T.E.1
  • 17
    • 0030367389 scopus 로고    scopus 로고
    • An eighth order method with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem
    • Simos T.E. An eighth order method with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem Internat. J. Modern Phys. C 7 1996 825-835
    • (1996) Internat. J. Modern Phys. C , vol.7 , pp. 825-835
    • Simos, T.E.1
  • 18
    • 0031326292 scopus 로고    scopus 로고
    • Eighth order methods with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem
    • Simos T.E. Eighth order methods with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem J. Math. Chem. 21 1997 359-372
    • (1997) J. Math. Chem. , vol.21 , pp. 359-372
    • Simos, T.E.1
  • 19
    • 0032380346 scopus 로고    scopus 로고
    • An eighth order exponentially-fitted method for the numerical solution of the Schrödinger equation
    • Simos T.E. An eighth order exponentially-fitted method for the numerical solution of the Schrödinger equation Internat. J. Modern Phys. C 9 1998 271-288
    • (1998) Internat. J. Modern Phys. C , vol.9 , pp. 271-288
    • Simos, T.E.1
  • 20
    • 0001190986 scopus 로고    scopus 로고
    • New embedded explicit methods with minimal phase-lag for the numerical integration of the Schrödinger equation
    • Simos T.E. New embedded explicit methods with minimal phase-lag for the numerical integration of the Schrödinger equation Comput. Chem. 22 1998 433-440
    • (1998) Comput. Chem. , vol.22 , pp. 433-440
    • Simos, T.E.1
  • 21
    • 0345831862 scopus 로고    scopus 로고
    • High algebraic order methods with minimal phase-lag for accurate solution of the Schrödinger equation
    • Simos T.E. High algebraic order methods with minimal phase-lag for accurate solution of the Schrödinger equation Internat. J. Modern Phys. C 9 1998 1055-1071
    • (1998) Internat. J. Modern Phys. C , vol.9 , pp. 1055-1071
    • Simos, T.E.1
  • 22
    • 0033148222 scopus 로고    scopus 로고
    • Explicit eighth order methods for the numerical integration of initial-value problems with periodic or oscillating solutions
    • Simos T.E. Explicit eighth order methods for the numerical integration of initial-value problems with periodic or oscillating solutions Comput. Phys. Comm. 119 1999 32-44
    • (1999) Comput. Phys. Comm. , vol.119 , pp. 32-44
    • Simos, T.E.1
  • 23
    • 0013350031 scopus 로고    scopus 로고
    • Atomic Structure Computations in Chemical Modelling: Applications and Theory
    • A. Hinchliff (Ed.)
    • T.E. Simos, in: A. Hinchliff (Ed.), Atomic Structure Computations in Chemical Modelling: Applications and Theory, UMIST, The Royal Society of Chemistry, 2000, pp. 38-142.
    • (2000) UMIST, The Royal Society of Chemistry , pp. 38-142
    • Simos, T.E.1
  • 24
    • 0025596658 scopus 로고
    • Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation
    • Simos T.E. Raptis A.D. Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation Computing 45 1990 175-181
    • (1990) Computing , vol.45 , pp. 175-181
    • Simos, T.E.1    Raptis, A.D.2
  • 25
    • 0031101965 scopus 로고    scopus 로고
    • A finite-difference method for the numerical solution of the Schrödinger equation
    • Simos T.E. Williams P.S. A finite-difference method for the numerical solution of the Schrödinger equation J. Comput. Appl. Math. 79 1997 189-205
    • (1997) J. Comput. Appl. Math. , vol.79 , pp. 189-205
    • Simos, T.E.1    Williams, P.S.2
  • 26
    • 0001590149 scopus 로고    scopus 로고
    • Bessel and Neumann fitted methods for the numerical solution of the radial Schrödinger equation
    • Simos T.E. Williams P.S. Bessel and Neumann fitted methods for the numerical solution of the radial Schrödinger equation J. Comput. Chem. 21 1997 175-179
    • (1997) J. Comput. Chem. , vol.21 , pp. 175-179
    • Simos, T.E.1    Williams, P.S.2
  • 27
    • 0021316047 scopus 로고
    • Phase properties of high order, almost P-stable formulae
    • Thomas R.M. Phase properties of high order, almost P-stable formulae BIT 24 1994 225-238
    • (1994) BIT , vol.24 , pp. 225-238
    • Thomas, R.M.1
  • 28
    • 0035315407 scopus 로고    scopus 로고
    • A family of P-stable eighth algebraic order methods with exponential fitting facilities
    • Vigo-Aguiar J. Simos T.E. A family of P-stable eighth algebraic order methods with exponential fitting facilities J. Math. Chem. 29 2001 177
    • (2001) J. Math. Chem. , vol.29 , pp. 177
    • Vigo-Aguiar, J.1    Simos, T.E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.