A sixth order Bessel and Neumann fitted method for the numerical solution of the Schrödinger equation

Molecular Simulation

Volumn 21, Issue 4, 1999, Pages 191-204

  Simos, T E ^a  

^a DEMOCRITUS UNIVERSITY OF THRACE   (Greece)

Author keywords

Bessel and neumann fitting; Coupled differential equations; Scattering problems; Schr dinger equation

Indexed keywords

EID: 0004407841     PISSN: 08927022     EISSN: None     Source Type: Journal    
DOI: 10.1080/08927029908022061     Document Type: Article

References (17)

1. Allison, A. C. (1970). The numerical solution of coupled differential equations arising from the Schrödinger equation, J. Comput. Phys., 6, 378-391.
2. Avdelas, G. and Simos, T. E. (1996). A generator of high-order embedded P-stable methods for the numerical solution of the Schrödinger equation, J. Comput. Appl. Math., 72, 345-358.
3. Avdelas, G. and Simos, T. E. (1996). Embedded methods for the numerical solution of the Schrödinger equation, Comput. Math. Appl., 31, 85-102.
4. Ixaru, L. Gr., Rizea, M. and Vertse, T. (1995). Piecewise perturbation methods for calculating eigensolutions of a complex optical potential, Comput. Phys. Commun., 85, 217-230.
5. Landau, L. D. and Lifshitz, F. M., Quantum Mechanics (Pergamon, New York, 1965).
6. Raptis, A. D. and Allison, A. C. (1978). Exponential-fitting methods for the numerical solution of the Schrödinger equation, Comput. Phys. Commun., 14, 1-5.
7. Raptis, A. D. (1977). Numerical solution of coupled differential equations, Ph. D. Thesis, Glasgow University, Glasgow.
8. Raptis, A. D. and Cash, J. R. (1985). A variable-step method for the numerical integration of the one-dimensional Schrödinger equation, Comput. Phys. Commun., 36, 113-119.
9. Raptis, A. D. and Cash, J. R. (1987). Exponential and Bessel fitting methods for the numerical solution of the Schrödinger equation, Comput. Phys. Commun., 44, 95-103.
10. Shampine, L. F., Watts, H. A. and Davenport, S. M. (1976). Solving nonstiff ordinary differential equations - The state of the art, SIAM Rev., 18, 376-411.
11. Simos, T. E. (1992). Exponential fitted methods for the numerical integration of the Schrödinger equation, Comput. Phys. Commun., 71, 32-38.
12. Simos, T. E. (1993). New variable-step procedure for the numerical integration of the one-dimensional Schrödinger equation, J. Comput. Phys., 108, 175-179.
13. Simos, T. E. and Mousadis, G. (1994). A two-step method for the numerical solution of the radial Schrödinger equation, Comput. Math. Appl., 83, 1145-1153.
14. Thomas, L. D., Alexander, M. H., Johmson, B. R., Lester, W. A. Jr., Light, J. C., McLenithan, K. D., Parker, G. A., Redmon, M. J., Schmaltz, T. G., Secrest, D. and Walker, R. B. (1981). Comparison of numerical methods for solving second order differential equations of molecular scattering theory, J. Comput. Phys., 41, 401-426.
15. Simos, T. E. and Williams, P. S. (1997). Bessel and Neumann-fitted methods for the numerical solution of the radial Schrödinger equation, Computers Chemistry, 21, 175-179.
16. Bernstein, R. B., Dalgarno, A., Massey, H. and Percival, I. C. (1963). Thermal scattering of atoms by homonuclear diatomic molecules, Proc. Roy. Soc. Ser. A, 274, 427-442.
17. Bernstein, R. B. (1960). Quantum mechanical (phase shift) analysis of differential elastic scattering of molecular beams, J. Chem. Phys., 33, 795-804.