A relaxation method for nonlocal and non-Hermitian operators

Journal of Computational Physics

Volumn 126, Issue 1, 1996, Pages 229-236

  Lagaris, I E ^a,b   Papageorgiou, D G ^a,b   Braun, M ^a   Sofianos, S A ^a  

^a UNIVERSITY OF SOUTH AFRICA   (South Africa)

^b UNIVERSITY OF IOANNINA   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; LINEAR SYSTEMS; TIME DOMAIN ANALYSIS;

CRANK-NICHOLSON SCHEME; DERIVATIVE OPERATORS; GRID METHODS; HERMITIAN OPERATORS; HERMITIANS; NONLOCAL OPERATOR; RELAXATION METHODS; SPARSE LINEAR SYSTEMS; SYMMETRICS; TIME DEPENDENT;

HAMILTONIANS;

EID: 0030160715     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1996.0131     Document Type: Article

References (46)

1. 1. Y. C. Tang and K. Wildermuth, A Unified Theory of Nucleus (Vieweg, Brunswick, 1977).
2. 2. D. R. Thompson, I. Reichstein, W. McClure, and Y. C. Tang, Phys. Rev. 185, 1351 (1969).
3. 3. G. L. Payne, in Models and Methods in Few-Body Physics, Lecture Notes in Physics, Vol. 273, edited by L. S. Fereira, A. C. Fonseca, and L. Streit (Springer-Verlag, New York, 1987), p. 64.
4. 4. M. Fabre de la Ripelle, H. Fiedeldey, and S. A. Sofianos, Phys. Rev. C 38, 449 (1988).
5. 5. H. de Raedt, Comput. Phys. Rep. 7, 1 (1987).
6. 6. R. B. Gerber, R. Kosloff, and M. Berman, Comput. Phys. Rep. 5, 59 (1986).
7. 7. A. A. Kvitsinsky and C. Y. Hu, Few-body Systems 12, 7 (1992).
8. 8. M. G. Cox, J. Inst. Math. Appl. 10, 134 (1972).
9. 9. R. Mceeny and B. T. Sutcliffe, Comput. Phys. Rep. 2, 217 (1985).
10. 10. C. F. Fischer, Comput. Phys. Rept. 3, 273 (1986); L. Laaksonen, P. Pyykko, and D. Sundholm, Comput. Phys. Rep. 4, 313 (1986); R. Mc Weeny and B. T. Sutcliffe, Comput. Phys. Rep. 2, 217 (1984).
11. 10. C. F. Fischer, Comput. Phys. Rept. 3, 273 (1986); L. Laaksonen, P. Pyykko, and D. Sundholm, Comput. Phys. Rep. 4, 313 (1986); R. Mc Weeny and B. T. Sutcliffe, Comput. Phys. Rep. 2, 217 (1984).
12. 10. C. F. Fischer, Comput. Phys. Rept. 3, 273 (1986); L. Laaksonen, P. Pyykko, and D. Sundholm, Comput. Phys. Rep. 4, 313 (1986); R. Mc Weeny and B. T. Sutcliffe, Comput. Phys. Rep. 2, 217 (1984).
13. 11. S. Carter and N. C. Handy, Comput. Phys. Rep. 5, 115 (1986).
14. 12. K. E. Schmidt and M. H. Kalos, "Application of the Monte-Carlo Methods in Statistical Physics," in Topics in Current Physics, Vol. 36, edited by K. Binder (Springer-Verlag, New York/Berlin, 1984).
15. 13. R. A. Friesner, Annu. Rev. Chem. 42, 341 (1991).
16. 14. Z. Ba čić and J. C. Light, Annu. Rev. Chem. 40, 440 (1989); R. W. Heather and J. C. Light, J. Chem. Phys. 79, 147 (1983); J. V. Lill, G. A. Parker, and J. C. Light, J. Chem. Phys. 85, 901 (1986).
17. 14. Z. Ba čić and J. C. Light, Annu. Rev. Chem. 40, 440 (1989); R. W. Heather and J. C. Light, J. Chem. Phys. 79, 147 (1983); J. V. Lill, G. A. Parker, and J. C. Light, J. Chem. Phys. 85, 901 (1986).
18. 14. Z. Ba čić and J. C. Light, Annu. Rev. Chem. 40, 440 (1989); R. W. Heather and J. C. Light, J. Chem. Phys. 79, 147 (1983); J. V. Lill, G. A. Parker, and J. C. Light, J. Chem. Phys. 85, 901 (1986).
19. 15. M. Braun, S. A. Sofianos, D. G. Papageorgiou, and I. E. Lagaris, J. Comput. Phys. 125(2), (1996).
20. 16. R. Kosloff and H. Tal-Ezer, Chem. Phys. Lett. 127, 223 (1986).
21. 17. D. Neuhauser, J. Chem. Phys. 93, 2611 (1990); 100, 5076 (1994).
22. 17. D. Neuhauser, J. Chem. Phys. 93, 2611 (1990); 100, 5076 (1994).
23. 18. R. E. Wyatt, Phys. Rev. E 51, 3643 (1995).
24. 19. R. Schinke, Photodissociation Dynamics: Spectroscopy and Fragmentation of Small Polyatomic Molecules (Cambridge Univ. Press, Cambridge, 1993).
25. 20. G. D. Smith, Numerical Solution of Partial Differential Equations (Clarendon Press, Oxford, 1985).
26. 21. A. Goldberg, H. M. Schey, and J. J. Schwartz, Am. J. Phys. 35, 177 (1967).
27. 22. D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing (Brooks/Cole, Pacific Grove, CA, 1991).
28. 23. R. S. Varga, Matrix Iterative Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1962).
29. 24. G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins Press, Baltimore, 1993).
30. 25. H. W. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge Univ. Press, Cambridge, 1992).
31. 26. R. A. Malfliet and J. A. Tjon, Nucl. Phys. A 127, 161 (1969); Ann. Phys. (N.Y.) 61, 425 (1970).
32. 26. R. A. Malfliet and J. A. Tjon, Nucl. Phys. A 127, 161 (1969); Ann. Phys. (N.Y.) 61, 425 (1970).
33. 27. T. Kaneko, M. LeMere, and Y. C. Tang, Phys. Rev. C 44, 1588 (1991).
34. 28. M. Fabre de la Ripelle, M. I. Haftel, and S. Y. Larsen, Phys. Rev. A 44, 7084 (1991).
35. 29. M. Fabre de la Ripelle, in Models and Methods in Few-Body Physics, Lecture Notes in Physics, Vol. 273, edited by L. S. Fereira, A. C. Fonseca, and L. Streit (Springer-Verlag, New York, 1987), p. 283.
36. 30. M. Fabre de la Ripelle, H. Fiedeldey, and S. A. Sofianos, Few-Body Systems 6, 157 (1989).
37. 31. W. Oehm, S. A. Sofianos, H. Fiedeldey, and M. Fabre de la Ripelle, Phys. Rev. C 42, 2322 (1990).
38. 32. W. Oehm, S. A. Sofianos, H. Fiedeldey, and M. Fabre de la Ripelle, Phys. Rev. C 43, 25 (1991).
39. 33. W. Oehm, S. A. Sofianos, H. Fiedeldey, and M. Fabre la Ripelle, Phys. Rev. C 44, 81 (1991).
40. 34. G. Erens, J. L. Viechers, and R. van Wageningen, Ann. Phys. (N.Y.) 67, 461 (1971).
41. 35. S. Fantoni, L. Panattoni, and S. Rosati, Nuovo Cimento A 69, 81 (1970).
42. 36. J. G. Zabolitsky, in Progress in Particle and Nuclear Physics, edited by A. Faessler (Pergamon, New York, 1986), Vol. 16, p. 103.
43. 37. J. L. Friar, Few-body Syst. Suppl. 2, 51 (1957).
44. 38. I. R. Afnan and Y. C. Tang, Phys. Rev. A 175, 1337 (1968).
45. 39. J. L. Ballot, Z. Phys. A 302, 347 (1981).
46. 40. J. J. Dongarra, University of Tennessee Report CS-89-85, 1995 (unpublished).