메뉴 건너뛰기




Volumn 182, Issue 1, 2006, Pages 559-566

Energy spectra of the Schrödinger equation and the differential quadrature method: Improvement of the solution using particle swarm optimization

Author keywords

Bound; Particle swarm; Quadratic; Spectra

Indexed keywords

DIFFERENTIAL EQUATIONS; INTERPOLATION; NUMERICAL METHODS; OPTIMIZATION;

EID: 33750803269     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.04.018     Document Type: Article
Times cited : (6)

References (33)
  • 2
    • 11144349235 scopus 로고    scopus 로고
    • A generalized integral quadratic method: I. An efficient solution for one-dimensional Volterra integral equation
    • Zerarka A., and Soukeur A. A generalized integral quadratic method: I. An efficient solution for one-dimensional Volterra integral equation. Commun. Nonlinear Sci. Numer. Simul. 10 (2005) 653-663
    • (2005) Commun. Nonlinear Sci. Numer. Simul. , vol.10 , pp. 653-663
    • Zerarka, A.1    Soukeur, A.2
  • 3
    • 0039398395 scopus 로고
    • Algebraic methods in quantum mechanics with applications to nuclear and molecular structure
    • Iachello F. Algebraic methods in quantum mechanics with applications to nuclear and molecular structure. Nucl. Phys. A 560 (1993) 23-34
    • (1993) Nucl. Phys. A , vol.560 , pp. 23-34
    • Iachello, F.1
  • 4
    • 0035510391 scopus 로고    scopus 로고
    • Numerically complemented analytic method for solving the time-independent one-dimensional Schrödinger equation
    • Selg M. Numerically complemented analytic method for solving the time-independent one-dimensional Schrödinger equation. Phys. Rev. E 64 5 (2001) 056701
    • (2001) Phys. Rev. E , vol.64 , Issue.5 , pp. 056701
    • Selg, M.1
  • 5
    • 0034349252 scopus 로고    scopus 로고
    • Exact solutions of the two-dimensional Schrödinger equation with certain central potentials
    • Dong S.H. Exact solutions of the two-dimensional Schrödinger equation with certain central potentials. Int. J. Theor. Phys. 39 (2000) 1119
    • (2000) Int. J. Theor. Phys. , vol.39 , pp. 1119
    • Dong, S.H.1
  • 6
    • 0010292273 scopus 로고    scopus 로고
    • Exact solution of nonrelativistic Schrödinger equation for certain central physical potentials
    • Bose S.K., and Gupta N. Exact solution of nonrelativistic Schrödinger equation for certain central physical potentials. IL Nuovo Cimento B 113 (1998) 299
    • (1998) IL Nuovo Cimento B , vol.113 , pp. 299
    • Bose, S.K.1    Gupta, N.2
  • 7
    • 0000066461 scopus 로고
    • Eigenstates and oscillator strengths for the Hulthén potential
    • Varshni Y.P. Eigenstates and oscillator strengths for the Hulthén potential. Phys. Rev. A 41 (1990) 4682
    • (1990) Phys. Rev. A , vol.41 , pp. 4682
    • Varshni, Y.P.1
  • 8
    • 0000698580 scopus 로고    scopus 로고
    • Shifted 1/N expansion for confined quantum systems
    • Sinha A., Roychoudhury R., and Varshni Y.P. Shifted 1/N expansion for confined quantum systems. Can. J. Phys. 78 (2000) 141
    • (2000) Can. J. Phys. , vol.78 , pp. 141
    • Sinha, A.1    Roychoudhury, R.2    Varshni, Y.P.3
  • 9
    • 0030194371 scopus 로고    scopus 로고
    • An efficient Chebyshev-Lanczos method for obtaining eigensolutions of the Schrödinger equation on a grid
    • Braun M., Sofianos S.A., Papageorgiou D.G., and Lagaris I.E. An efficient Chebyshev-Lanczos method for obtaining eigensolutions of the Schrödinger equation on a grid. J. Comput. Phys. 126 (1996) 315
    • (1996) J. Comput. Phys. , vol.126 , pp. 315
    • Braun, M.1    Sofianos, S.A.2    Papageorgiou, D.G.3    Lagaris, I.E.4
  • 11
    • 0034682679 scopus 로고    scopus 로고
    • Quantum states of a sextic potential: hidden symmetry and quantum monodromy
    • Child M.S., Dong S.H., and Wang X.G. Quantum states of a sextic potential: hidden symmetry and quantum monodromy. J. Phys. A: Math. Gen. 33 (2000) 5653
    • (2000) J. Phys. A: Math. Gen. , vol.33 , pp. 5653
    • Child, M.S.1    Dong, S.H.2    Wang, X.G.3
  • 12
    • 21844481156 scopus 로고
    • The exact solution of two new types of Schrödinger equation
    • Exton H. The exact solution of two new types of Schrödinger equation. J. Phys. A: Math. Gen. 28 (1995) 6739
    • (1995) J. Phys. A: Math. Gen. , vol.28 , pp. 6739
    • Exton, H.1
  • 14
    • 0004067381 scopus 로고
    • Oxford University Press, Oxford
    • Maitland, et al. Intermolecular Forces (1987), Oxford University Press, Oxford
    • (1987) Intermolecular Forces
    • Maitland1
  • 16
    • 12144268141 scopus 로고
    • Diatomic molecules according to the wave mechanics. II. Vibrational levels
    • Morse P.M. Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys. Rev. 34 (1929) 57
    • (1929) Phys. Rev. , vol.34 , pp. 57
    • Morse, P.M.1
  • 17
    • 0141451680 scopus 로고    scopus 로고
    • Quantum monodromy of Schrödinger equation with the decatic potential
    • Dong S.H. Quantum monodromy of Schrödinger equation with the decatic potential. Int. J. Theor. Phys. 41 1 (2002) 89-99
    • (2002) Int. J. Theor. Phys. , vol.41 , Issue.1 , pp. 89-99
    • Dong, S.H.1
  • 18
    • 0029517385 scopus 로고    scopus 로고
    • R.C. Eberhart, J. Kennedy, A new optimizer using particles swarm theory, in: Sixth International Symposium on Micro Machine and Human Science, Nagoya, Japan, 1995, pp. 39-43.
  • 20
    • 33750826458 scopus 로고    scopus 로고
    • K.E. Parsopoulos, V.P. Plagianakos, G.D. Magoulas, M.N. Vrahatis, Stretching technique for obtaining global minimizers through particle swarm optimization, in: Proceedings of the PSO Workshop, Indianapolis, USA, 2001, 22-29.
  • 21
    • 0002189485 scopus 로고    scopus 로고
    • Modification of the particle swarm optimizer for locating all the global minima
    • Kurkova V., et al. (Ed), Springer
    • Parsopoulos K.E., and Vrahatis M.N. Modification of the particle swarm optimizer for locating all the global minima. In: Kurkova V., et al. (Ed). Artificial Neural Networks and Genetic Algorithms (2001), Springer 324-327
    • (2001) Artificial Neural Networks and Genetic Algorithms , pp. 324-327
    • Parsopoulos, K.E.1    Vrahatis, M.N.2
  • 22
    • 33750806946 scopus 로고    scopus 로고
    • P.C. Fourie, A.A. Groenwold, Particle swarms in topology optimization, Extended Abstracts of the Fourth World Congress of Structural and Multidisciplinary Optimization, Dalian, China, June 4-8, 2001, pp. 52-53.
  • 23
    • 33750832192 scopus 로고    scopus 로고
    • P.C. Fourie, A.A. Groenwold, Particle swarms in size and shape optimization, in: Proceedings of the International Workshop on Multidisciplinary Design Optimization, Pretoria, South Africa, August 7-10, 2000, pp. 97-106.
  • 25
    • 37049013963 scopus 로고    scopus 로고
    • The behavior of particles
    • Kennedy J. The behavior of particles. Evol. Prog. VII (1998) 581-587
    • (1998) Evol. Prog. , vol.VII , pp. 581-587
    • Kennedy, J.1
  • 27
    • 0034869626 scopus 로고    scopus 로고
    • Y.H. Shi, R.C. Eberhart, Fuzzy adaptive particle swarm optimization, in: IEEE Int. Conf. on Evolutionary Computation, 2001, pp. 101-106.
  • 28
    • 0031674071 scopus 로고    scopus 로고
    • J. Kennedy, W.M. Spears, Matching algorithms to problems: an experimental test of the particle swarm and some genetic algorithms on the multimodal problem generator, in: Proceedings of the 1998 IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, May 4-9, 1998.
  • 29
    • 0031700696 scopus 로고    scopus 로고
    • Y. Shi, R.C.A. Eberhart, Modified particle swarm optimizer, in: Proceedings of the 1998 IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, May 4-9, 1998.
  • 30
    • 84879015433 scopus 로고    scopus 로고
    • Parameter selection in particle swarm optimization. Evolutionary programming VII
    • Shi Y.H., and Eberhart R.C. Parameter selection in particle swarm optimization. Evolutionary programming VII. Lect. Notes Comput. Sci. (1998) 591-600
    • (1998) Lect. Notes Comput. Sci. , pp. 591-600
    • Shi, Y.H.1    Eberhart, R.C.2
  • 31
    • 84901421400 scopus 로고    scopus 로고
    • M. Clerc, The swarm and the queen: towards a deterministic and adaptive particle swarm optimization, in: Proceedings of the 1999 IEEE Congress on Evolutionary Computation, Washington DC, 1999, pp. 1951-1957.
  • 32
    • 84879015433 scopus 로고    scopus 로고
    • Parameter selection in particle swarm optimization
    • Porto V.W., Saravanan N., Waagen D., and Eiben A.E. (Eds), Springer
    • Eberhart R.C., and Shi Y. Parameter selection in particle swarm optimization. In: Porto V.W., Saravanan N., Waagen D., and Eiben A.E. (Eds). Lecture Notes in Computer Science-Evolutionary Programming VII vol. 1447 (1998), Springer 591-600
    • (1998) Lecture Notes in Computer Science-Evolutionary Programming VII , vol.1447 , pp. 591-600
    • Eberhart, R.C.1    Shi, Y.2
  • 33
    • 0037475094 scopus 로고    scopus 로고
    • The particle swarm optimization algorithm: convergence analysis and parameter selection
    • Cristian T.I. The particle swarm optimization algorithm: convergence analysis and parameter selection. Inform. Process. Lett. 85 6 (2003) 317-325
    • (2003) Inform. Process. Lett. , vol.85 , Issue.6 , pp. 317-325
    • Cristian, T.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.