A finite difference continuation method for computing energy levels of Bose-Einstein condensates

Computer Physics Communications

Volumn 179, Issue 4, 2008, Pages 208-226

  Chang, S L ^a   Chien, C S ^b   Li, Z C ^c  

^a SOUTHERN TAIWAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Taiwan)

^b NATIONAL CHUNG HSING UNIVERSITY   (Taiwan)

^c NATIONAL SUN YAT SEN UNIVERSITY   (Taiwan)

Author keywords

Continuation methods; Finite difference method; Nonlinear Schr dinger equation; Superconvergence; Superfluid densities

Indexed keywords

BOSE-EINSTEIN CONDENSATION; DIFFERENCE EQUATIONS; DIFFERENTIATION (CALCULUS); EIGENVALUES AND EIGENFUNCTIONS; ELECTRIC NETWORK TOPOLOGY; ELECTRON ENERGY LEVELS; FINITE ELEMENT METHOD; FREQUENCY DIVISION MULTIPLEXING; FUNCTION EVALUATION; MATERIALS SCIENCE; NUMERICAL ANALYSIS; NUMERICAL METHODS; ORTHOGONAL FREQUENCY DIVISION MULTIPLEXING; SOLUTIONS; STEAM CONDENSERS; SWITCHING SYSTEMS; WAVE FUNCTIONS;

(001) PARAMETER; (MIN ,MAX ,+) FUNCTIONS; BOSE-EINSTEIN CONDENSATE (BEC); BOSE-EINSTEIN CONDENSATES (BECS); CONTINUATION METHODS; EIGENVALUE PROBLEM (EVP); ENERGY LEVELS; EXCITED-STATES; FINITE DIFFERENCE (FD); FINITE DIFFERENCE METHOD (FDM); FINITE ELEMENT (FE); GROSS-PITAEVSKII EQUATION (GPE); GROUND STATE (GS); MATHEMATICAL THEORIES; NUMERICAL SOLUTIONS; SECOND ORDERS; SUPER CONVERGENCE; VARIATIONAL FORM;

FINITE DIFFERENCE METHOD;

EID: 47349105007     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2008.02.014     Document Type: Article

References (43)

1. Anderson M.H., Ensher J.R., Matthews M.R., and Wieman C.E. Science 269 (1995) 198
2. Davis K.B., Mewes M.-O., Andrews M.R., van Druten N.J., Durfee D.S., Kurn D.M., and Ketterle W. Phys. Rev. Lett. 75 (1995) 3969
3. Bradley C.C., Sackett C.A., Tollett J.J., and Hulet R.G. Phys. Rev. Lett. 75 (1995) 1687
4. García-Ripoll J.J., and Pérez-García V.M. SIAM J. Sci. Comput. 23 (2001) 1316
5. Bao W., and Du Q. SIAM J. Sci. Comput. 25 (2004) 1674
6. Bao W. Multiscale Model. Simul. 2 (2004) 210
7. Bao W., and Tang W. J. Comput. Phys. 187 (2003) 230
8. Li Z.C., Yamamoto T., and Fang Q. J. Comp. Appl. Math. 151 (2003) 307
9. Babuska I., and Osborn J. Eigenvalue problems. Finite Element Methods. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of Numerical Analysis vol. II (1991), North-Holland, Amsterdam 641-787 (Part I)
10. Myatt C.J., Burt E.A., Ghrist R.W., Cornel E.A., and Wieman C.E. Phys. Rev. Lett. 78 (1997) 586
11. Hall D.S., Matthews M.R., Ensher J.R., Wieman C.E., and Cornell E.A. Phys. Rev. Lett. 81 (1998) 1539
12. Gross E.P. Nuovo Cimento 20 (1961) 454
13. Pitaevskii L.P. Zh. Eksp. Teor. Fiz. 40 (1961) 646
14. Pitaevskii L.P. Sov. Phys. JETP 13 (1961) 451
15. Chang S.-L., Chien C.-S., and Jeng B.-W. SIAM J. Sci. Comput. 29 (2007) 729
16. Chang S.-L., Chien C.-S., and Jeng B.-W. J. Comput. Phys. 226 (2007) 104
17. Chang S.-L., and Chien C.-S. Comput. Phys. Comm. 177 (2007) 707
18. Allgower E.L., and Georg K. Introduction to Numerical Continuation Methods (2003), SIAM, Philadelphia, PA
19. Govaerts W.J.F. Numerical Methods for Bifurcation Problems of Dynamical Equilibria (2000), SIAM, Philadelphia, PA
20. Keller H.B. Lectures on Numerical Methods in Bifurcation Problems (1987), Springer-Verlag, Berlin
21. Rheinboldt W.C. Numerical Analysis of Parametrized Nonlinear Equations (1986), John Wiley, New York
22. Chang S.-L., Chien C.-S., and Jeng B.-W. Inter. J. Bifurcation Chaos 15 (2005) 2689
23. Stamper-Kurn D.M., Andrews M.R., Chikkatur A.P., Inouye S., Miesner H.J., Stenger J., and Ketterle W. Phys. Rev. Lett. 80 (1998) 2027
24. Chen G.-H., and Wu Y.-S. Phys. Rev. A 67 (2003) 013606
25. Jaksch T., Gardiner S.A., Schulze K., Cirac J.I., and Zoller P. Phys. Rev. Lett. 86 (2001) 4733
26. Chang S.M., Lin W.W., and Shieh S.F. J. Comput. Phys. 202 (2005) 367
27. Chang S.-L., and Chien C.-S. Inter. J. Bifurcation Chaos 17 (2007) 641
28. Bramble J.H., and Hubbard B.E. Numer. Math. 4 (1962) 313
29. Matsunaga N., and Yamamoto T. J. Comp. Appl. Math. 116 (2000) 263
30. Li Z.C., Hu H.Y., Fang Q., and Yamamoto T. Numer. Funct. Anal. Optim. 24 (2003) 195
31. Li Z.C., Hu H.Y., Wang S., and Fang Q. Appl. Numer. Math. (2008)
32. Chien C.-S., and Chang S.-L. Numer. Linear Algebra Appl. 10 (2003) 335
33. Bao W., and Jaksch D. SIAM J. Numer. Anal. 41 (2003) 1406
34. Bao W., Huang H., and Markowich P.A. Comm. Math. Sci. 3 (2007) 57
35. D.J. Hahn, Private communication, 2007
36. Caloz G., and Rappaz J. Numerical Analysis for Nonlinear and Bifurcation Problems. In: Ciarlet P.G., and Lions J.L. (Eds). Handbook of Numerical Analysis vol. V (1997), Elsevier Science B.V. 487
37. Chien C.-S., Huang H.T., Jeng B.-W., and Li Z.C. Inter. J. Bifurcation Chaos (2007)
38. Li Z.C., Fang Q., Wang S., and Hu H.Y. Numer. Funct. Anal. Optim. (2007)
39. Li Z.C. Numer. Methods for P.D.E. 5 (1989) 279
40. Li Z.C. J. Comp. Appl. Math. 87 (1997) 1
41. Li Z.C. Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities (1998), Kluwer Academic Publishers, Bordrecht, Boston, London
42. Simpson R.B. SIAM J. Numer. Anal. 118 (1972) 359
43. Ciarlet P.G. In: Ciarlet P.G., and Lions J.L. (Eds). Finite Element Methods (1991), North-Holland, Amsterdam 17 (Part 1)