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Volumn 22, Issue 4-5, 1999, Pages 303-349

High algebraic order methods for the numerical solution of the Schrödinger equation

Author keywords

Bessel and Neumann fitting; Coupled differential equations; Eigenvalue problems; Exponential fitting; Finite differences; Multistep methods; Phase shift problems; Phase lag; Resonance problems; Scattering problems; Schr dinger equation

Indexed keywords


EID: 26644470130     PISSN: 08927022     EISSN: None     Source Type: Journal    
DOI: 10.1080/08927029908022103     Document Type: Article
Times cited : (3)

References (31)
  • 1
    • 0001424633 scopus 로고    scopus 로고
    • A Numerov-type method for computing eigenvalues and resonances of the radial Schrödinger equation
    • Simos, T. E. and Tougelidis, G. (1996). A Numerov-type method for computing eigenvalues and resonances of the radial Schrödinger equation, Computers and Chemistry, 20, 397-401.
    • (1996) Computers and Chemistry , vol.20 , pp. 397-401
    • Simos, T.E.1    Tougelidis, G.2
  • 2
    • 84968515967 scopus 로고
    • An improved eigenvalue corrector formula for solving Schrödinger's equation for central fields
    • Cooley, J. W. (1961). An improved eigenvalue corrector formula for solving Schrödinger's equation for central fields, Mathematics of Computation, 15, 363-374.
    • (1961) Mathematics of Computation , vol.15 , pp. 363-374
    • Cooley, J.W.1
  • 3
    • 0000981521 scopus 로고
    • Practical points concerning the solution of the Schrödinger equation
    • Blatt, J. M. (1967). Practical points concerning the solution of the Schrödinger equation, Journal of Computational Physics, 1, 382-396.
    • (1967) Journal of Computational Physics , vol.1 , pp. 382-396
    • Blatt, J.M.1
  • 6
    • 0022752603 scopus 로고
    • A Numerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II. Explicit method
    • Chawla, M. M. and Rao, P. S. (1986). A Numerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II. Explicit method, Journal of Computational and Applied Mathematics, 15, 329-337.
    • (1986) Journal of Computational and Applied Mathematics , vol.15 , pp. 329-337
    • Chawla, M.M.1    Rao, P.S.2
  • 7
    • 0023315288 scopus 로고
    • An explicit sixth-order method with phase-lag of order eight for y″ = f(t, y)
    • Chawla, M. M. and Rao, P. S. (1987). An explicit sixth-order method with phase-lag of order eight for y″ = f(t, y), Journal of Computational and Applied Mathematics, 17, 365-368.
    • (1987) Journal of Computational and Applied Mathematics , vol.17 , pp. 365-368
    • Chawla, M.M.1    Rao, P.S.2
  • 8
    • 0040440161 scopus 로고
    • An explicit almost P-stable two-step method with phase-lag of order infinity for the numerical integration of second order periodic initial-values problems
    • Simos, T. E. (1992). An explicit almost P-stable two-step method with phase-lag of order infinity for the numerical integration of second order periodic initial-values problems, Applied Mathematics and Computation, 49, 261-268.
    • (1992) Applied Mathematics and Computation , vol.49 , pp. 261-268
    • Simos, T.E.1
  • 10
    • 0001330331 scopus 로고
    • Numerical methods for y″ = f(x, y) via rational approximation for the cosine
    • Coleman, J. P. (1989). Numerical methods for y″ = f(x, y) via rational approximation for the cosine, IMA Journal of Numerical Analysis, 9, 145-165.
    • (1989) IMA Journal of Numerical Analysis , vol.9 , pp. 145-165
    • Coleman, J.P.1
  • 11
    • 0023366337 scopus 로고
    • Explicit Runge-Kutta(-Nyström) methods with reduced phase errors for computing oscillating solutions
    • van der Houwen, P. J. and Sommeijer, B. P. (1987). Explicit Runge-Kutta(-Nyström) methods with reduced phase errors for computing oscillating solutions, SIAM Journal of Numerical Analysis, 24, 595-617.
    • (1987) SIAM Journal of Numerical Analysis , vol.24 , pp. 595-617
    • Van Der Houwen, P.J.1    Sommeijer, B.P.2
  • 12
    • 0021316047 scopus 로고
    • Phase properties of high order, almost P-stable formulae
    • Thomas, R. M. (1984). Phase properties of high order, almost P-stable formulae, BIT, 24, 225-238.
    • (1984) BIT , vol.24 , pp. 225-238
    • Thomas, R.M.1
  • 13
    • 0002586288 scopus 로고
    • Explicit two-step methods with minimal phase-lag for the numerical integration of special second order initial value problems and their application to the one-dimensional Schrödinger equation
    • Simos, T. E. (1992). Explicit two-step methods with minimal phase-lag for the numerical integration of special second order initial value problems and their application to the one-dimensional Schrödinger equation, Journal of Computational and Applied Mathematics, 39, 89-94.
    • (1992) Journal of Computational and Applied Mathematics , vol.39 , pp. 89-94
    • Simos, T.E.1
  • 14
    • 0040346415 scopus 로고    scopus 로고
    • A new Numerov-type method for computing eigenvalues and resonances of the radial Schrödinger equation
    • Simos, T. E. (1996). A new Numerov-type method for computing eigenvalues and resonances of the radial Schrödinger equation, International Journal of Modern Physics C, 7, 33-41.
    • (1996) International Journal of Modern Physics C , vol.7 , pp. 33-41
    • Simos, T.E.1
  • 15
    • 0031248617 scopus 로고    scopus 로고
    • Eighth order methods for accurate computations for the Schrödinger equation
    • Simos, T. E. (1997). Eighth order methods for accurate computations for the Schrödinger equation, Computer Physics Communications, 105, 127-138.
    • (1997) Computer Physics Communications , vol.105 , pp. 127-138
    • Simos, T.E.1
  • 16
    • 0021505273 scopus 로고
    • A high order method for the numerical solution of the one-dimensional Schrödinger equation
    • Cash, J. R. and Raptis, A. D. (1984). A high order method for the numerical solution of the one-dimensional Schrödinger equation, Computer Physics Communications, 33, 299-304.
    • (1984) Computer Physics Communications , vol.33 , pp. 299-304
    • Cash, J.R.1    Raptis, A.D.2
  • 17
    • 0001752844 scopus 로고
    • A variable step method for the numerical integration of the one-dimensional Schrödinger equation
    • Raptis, A. D. and Cash, J. R. (1985). A variable step method for the numerical integration of the one-dimensional Schrödinger equation, Computer Physics Communications, 36, 113-119.
    • (1985) Computer Physics Communications , vol.36 , pp. 113-119
    • Raptis, A.D.1    Cash, J.R.2
  • 20
    • 0016971912 scopus 로고
    • Solving non-stiff ordinary differential equations-the state of the art
    • Shampine, L. F., Watts, H. A. and Davenport, S. M. (1975). Solving non-stiff ordinary differential equations-the state of the art, SIAM Review, 18, 376-411.
    • (1975) SIAM Review , vol.18 , pp. 376-411
    • Shampine, L.F.1    Watts, H.A.2    Davenport, S.M.3
  • 21
    • 0001401038 scopus 로고
    • The numerical solution of coupled differential equations arising from the Schrödinger equation
    • Allison, A. C. (1970). The numerical solution of coupled differential equations arising from the Schrödinger equation, Journal of Computational Physics, 6, 378-391.
    • (1970) Journal of Computational Physics , vol.6 , pp. 378-391
    • Allison, A.C.1
  • 23
    • 0000633647 scopus 로고
    • Quantum mechanical (phase shift) analysis of differential elastic scattering of molecular beams
    • Bernstein, R. B. (1960). Quantum mechanical (phase shift) analysis of differential elastic scattering of molecular beams, Journal of Chemical Physics, 33, 795-804.
    • (1960) Journal of Chemical Physics , vol.33 , pp. 795-804
    • Bernstein, R.B.1
  • 24
    • 26644451576 scopus 로고
    • Ph.D. Thesis, Glasgow University, Glasgow
    • Allison, A. C. (1967). Ph.D. Thesis, Glasgow University, Glasgow.
    • (1967)
    • Allison, A.C.1
  • 25
    • 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. (1996). An eighth order method with minimal phase-lag for accurate computations for the elastic scattering phase-shift problem, International Journal of Modern Physics C, 7, 825-835
    • (1996) International Journal of Modern Physics C , vol.7 , pp. 825-835
    • Simos, T.E.1
  • 26
    • 2642543510 scopus 로고    scopus 로고
    • The renormalized Numerov method applied to calculating bound states of the coupled-channel Schrödinger equation
    • Johnson, B. R., The renormalized Numerov method applied to calculating bound states of the coupled-channel Schrödinger equation, Journal of Chemical Physics, 69, 4678-4688.
    • Journal of Chemical Physics , vol.69 , pp. 4678-4688
    • Johnson, B.R.1
  • 27
    • 0347069159 scopus 로고
    • An eighth order formula for the numerical integration of the one-dimensional Schrödinger equation
    • Allison, A. C., Raptis, A. D. and Simos, T. E. (1991). An eighth order formula for the numerical integration of the one-dimensional Schrödinger equation, Journal of Computational Physics, 97, 240-248.
    • (1991) Journal of Computational Physics , vol.97 , pp. 240-248
    • Allison, A.C.1    Raptis, A.D.2    Simos, T.E.3
  • 28
    • 0005354881 scopus 로고
    • An explicit high order predictor-corrector method for periodic initial-value problems
    • Simos, T. E. (1995). An explicit high order predictor-corrector method for periodic initial-value problems, Mathematical Models and Methods in Applied Sciences, 5, 159-166.
    • (1995) Mathematical Models and Methods in Applied Sciences , vol.5 , pp. 159-166
    • Simos, T.E.1
  • 29
    • 0000926830 scopus 로고
    • A four-step phase-fitted method for the numerical integration of second order initial-value problem
    • Raptis, A. D. and Simos, T. E. (1991). A four-step phase-fitted method for the numerical integration of second order initial-value problem, BIT, 31, 160-168.
    • (1991) BIT , vol.31 , pp. 160-168
    • Raptis, A.D.1    Simos, T.E.2
  • 31
    • 0032380346 scopus 로고    scopus 로고
    • An eighth order exponentially fitted method for the numerical solution of the Schrödinger equation
    • Simos, T. E. (1998). An eighth order exponentially fitted method for the numerical solution of the Schrödinger equation, International Journal of Modern Physics C, 9, 271-288.
    • (1998) International Journal of Modern Physics C , vol.9 , pp. 271-288
    • Simos, T.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.