Alternating direction implicit method for solving two-dimensional cubic nonlinear Schrödinger equation

Computer Physics Communications

Volumn 183, Issue 5, 2012, Pages 1082-1093

  Xu, Yiqiang ^a   Zhang, Luming ^a  

^a NANJING UNIVERSITY OF AERONAUTICS AND ASTRONAUTICS   (China)

Author keywords

Alternating direction implicit; Cubic nonlinear Schr dinger equation; Extrapolation technique; High order compact

Indexed keywords

ADI SCHEME; ALTERNATING DIRECTION IMPLICIT; ALTERNATING DIRECTION IMPLICIT METHOD; ALTERNATING DIRECTION IMPLICIT SCHEMES; COMPUTATION COSTS; COMPUTATIONAL COSTS; CRANK-NICOLSON; DIFFERENCE APPROXIMATION; DINGER EQUATION; EXTRAPOLATION TECHNIQUE; EXTRAPOLATION TECHNIQUES; FOURTH-ORDER; HIGH-ORDER; NONLINEAR TERMS; NUMERICAL EXPERIMENTS; REAL COEFFICIENTS; SOLUTION PROCEDURE; SPATIAL DISCRETIZATIONS; TRIDIAGONAL MATRICES; UNCONDITIONALLY STABLE;

EXTRAPOLATION; FOURIER ANALYSIS; LINEARIZATION; MATRIX ALGEBRA; TWO DIMENSIONAL;

NONLINEAR EQUATIONS;

EID: 84862813685     PISSN: 00104655     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cpc.2012.01.006     Document Type: Article

References (24)

1. E.P. Gross Structure of a quantized vortex in boson systems Nuovo Cimento 20 1961 454
2. B.P. Anderson, and M.A. Kasevich Macroscopic quantum interference from atomic tunnel arrays Science 282 1998 1686
3. E.W. Hagley, L. Deng, M. Kozuma, J. Wen, K. Helmerson, S.L. Rolston, and W.D. Phillips A well-collimated quasi-continuous atom laser Science 283 1999 1706
4. M. Kozuma, Y. Suzuki, T. Torii, Y. Sugiura, T. Kuga, E.W. Hagley, and L. Deng Phase-coherent amplification of matter waves Science 286 1999 2309
5. M.L. Chiofalo, and M.P. Tosi Output from Bose condensates in tunnel arrays: the role of mean-field interactions and of transverse confinement Phys. Lett. A 268 2000 406
6. Q.S. Chang, Erhui Jia, and W. Sun Difference schemes for solving the generalized nonlinear Schrödinger equation J. Comput. Phys. 148 1999 397 415
7. H.Q. Wang Numerical studies on the split-step finite difference method for nonlinear Schrödinger equations Appl. Math. Comput. 170 2005 17 35
8. M. Dehghan, and A. Taleei A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients Comput. Phys. Comm. 181 2010 43 51
9. M. Dehghan, and A. Shokri A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions Comput. Math. Appl. 54 2007 136 146 (Pubitemid 47008913)
10. A. Mohebbi, and M. Dehghan The use of compact boundary value method for the solution of two-dimensional Schrödinger equation J. Comput. Appl. Math. 225 2009 124 134
11. Z.C. Wang, and H.Z. Shao A new kind of discretization scheme for solving a two-dimensional time-independent Schrödinger equation Comput. Phys. Comm. 180 2009 842 849
12. G. Avdelas, A. Konguetsof, and T.E. Simos A generalization of Numerov's method for the numerical solution of the Schrödinger equation in two dimensions Comput. Chem. 24 2000 577 584
13. J. Vigo-Aguiar, and H. Ramos A variable-step Numerov method for the numerical solution of the Schrödinger equation J. Math. Chem. 37 2005 255 262 (Pubitemid 40584797)
14. J. Vigo-Aguiar, and T.E. Simos Review of multistep methods for the numerical solution of the radial Schrödinger equation Int. J. Quant. Chem. 103 2005 278 290 (Pubitemid 40751414)
15. S. Karaa, and J. Zhang High order ADI method for solving unsteady convection-diffusion problems J. Comput. Phys. 198 2004 1 9 (Pubitemid 38881868)
16. D. You A high-order Padé ADI method for unsteady convection-diffusion equations J. Comput. Phys. 214 2006 1 11 (Pubitemid 43300062)
17. Y. Jun, and T.Z. Mai ADI method-Domain decomposition Appl. Numer. Math. 56 2006 1092 1107
18. T.P. Witelski, and M. Bowenb ADI schemes for higher-order nonlinear diffusion equations Appl. Numer. Math. 45 2003 331 351
19. J.G. Qin The new alternating direction implicit difference methods for the wave equations J. Comput. Appl. Math. 230 2009 213 223
20. J.G. Qin The new alternating direction implicit difference methods for solving three-dimensional parabolic equations Appl. Math. Model. 34 2010 890 897
21. K.J. int' Hout, B.D. Welfert, and T.Z. Mai Unconditional stability of second-order ADI schemes applied to multi-dimensional diffusion equations with mixed derivative terms Appl. Numer. Math. 59 2009 677 692
22. Z.F. Tian, and P.X. Yu High-order compact ADI (HOC-ADI) method for solving unsteady 2D Schrödinger equation Comput. Phys. Comm. 181 2010 861 868
23. J.C. Li, Y.T. Chen, and G.Q. Liu High-order compact ADI methods for parabolic equations Comput. Math. Appl. 52 2006 1343 1356
24. Z.F. Tian, and Y.B. Ge A fourth-order compact ADI method for solving two-dimensional unsteady convection-diffusion problems J. Comput. Appl. Math. 198 2007 268 286 (Pubitemid 44345065)