Improved Lindstedt-Poincaré method for the solution of nonlinear problems

Journal of Sound and Vibration

Volumn 283, Issue 3-5, 2005, Pages 1115-1136

  Amore, Paolo ^a   Aranda, Alfredo ^a  

^a UNIVERSIDAD DE COLIMA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; OPTIMIZATION; PERTURBATION TECHNIQUES; PROBLEM SOLVING; QUANTUM THEORY;

ANHARMONIC OSCILLATORS; DUFFING EQUATION; LINEAR DELTA EXPANSION (LDE); NONLINEAR PROBLEMS;

OSCILLATORS (MECHANICAL);

EID: 15944389556     PISSN: 0022460X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsv.2004.06.009     Document Type: Article

References (17)

1. A. Lindstedt, Mem. de l'Ac. Imper. de St. Petersburg 31, 1883.
2. C.M. Bender, K.A. Milton, S.S. Pinsky, and L.M. Simmons A new perturbative approach to nonlinear problems Journal of Mathematical Physics 30 7 1989
3. C.M. Bender, and L.M.A. Bettencourt Multiple-scale analysis of quantum systems Physics Reviews D 54 1996 7710 [arXiv:hep-th/9607074]
4. A., Okopińska, Nonstandard expansion techniques for the effective potential in λ φ 4 quantum field theory, Physics Reviews D 35 (1987) 1835; A. Duncan, M. Moshe, Nonperturbative physics from interpolating actions, Physics Letters B 245 (1988) 352.
5. A., Okopińska, Nonstandard expansion techniques for the effective potential in λ φ 4 quantum field theory, Physics Reviews D 35 (1987) 1835; A. Duncan, M. Moshe, Nonperturbative physics from interpolating actions, Physics Letters B 245 (1988) 352.
6. M.P. Blencowe, and A.P. Korte Applying the linear delta expansion to disordered systems Physics Reviews B 56 1997 9422 [arXiv:cond-mat/9706260].
7. H.F. Jones, P. Parkin, and D. Winder Quantum dynamics of the slow rollover transition in the linear delta expansion Physics Reviews D 63 2001 125013 [arXiv:hep-th/0008069].
8. J.L. Kneur, M.B. Pinto, R.O. Ramos, Asymptotically improved convergence of optimized perturbation theory in the Bose-Einstein condensation problem, Physics Review A 68 (2003) 043615 [arXiv:cond-mat/0207295].
9. J.L. Kneur, M.B. Pinto, and R.O. Ramos Convergent resummed linear delta expansion in the critical O(N) (φ i 2) 3 d 2 model Physics Reviews Letters 89 2002 210403 [arXiv:cond-mat/0207089].
10. G. Krein, D.P. Menezes, and M.B. Pinto Optimized δ expansion for the Walecka model Physics Letters B 370 1996 5 [arXiv:nucl-th/9510059].
11. M.B. Pinto, and R.O. Ramos High temperature resummation in the linear delta-expansion Physics Reviews D 60 1999 105005 [arXiv:hep-ph/9903353].
12. P. Amore, and A. Aranda Presenting a new method for the solution of nonlinear problems Physics Letters A 316 2003 218 225 [arXiv:math-ph/0303042]
13. R. Guida, K. Konishi, H. Suzuki, Convergence of scaled delta expansion: anharmonic oscillator, Annals of Physics 241 (1995) 152 [arXiv:hep-th/9407027]; R. Guida, K. Konishi, H. Suzuki, Improved convergence proof of the delta expansion and order dependent mappings, Annals of Physics 249 (1996) 109 [arXiv:hep-th/9505084]; A. Duncan, H.F. Jones, Convergence proof for optimized delta expansion: the anharmonic oscillator, Physics Reviews D 47 (1993) 2560; I.R.C. Buckley, A. Duncan, H.F. Jones, Proof of the convergence of the linear delta expansion, Physics Reviews D 47 (1993) 2554.
14. R. Guida, K. Konishi, H. Suzuki, Convergence of scaled delta expansion: anharmonic oscillator, Annals of Physics 241 (1995) 152 [arXiv:hep-th/9407027]; R. Guida, K. Konishi, H. Suzuki, Improved convergence proof of the delta expansion and order dependent mappings, Annals of Physics 249 (1996) 109 [arXiv:hep-th/9505084]; A. Duncan, H.F. Jones, Convergence proof for optimized delta expansion: the anharmonic oscillator, Physics Reviews D 47 (1993) 2560; I.R.C. Buckley, A. Duncan, H.F. Jones, Proof of the convergence of the linear delta expansion, Physics Reviews D 47 (1993) 2554.
15. R. Guida, K. Konishi, H. Suzuki, Convergence of scaled delta expansion: anharmonic oscillator, Annals of Physics 241 (1995) 152 [arXiv:hep-th/9407027]; R. Guida, K. Konishi, H. Suzuki, Improved convergence proof of the delta expansion and order dependent mappings, Annals of Physics 249 (1996) 109 [arXiv:hep-th/9505084]; A. Duncan, H.F. Jones, Convergence proof for optimized delta expansion: the anharmonic oscillator, Physics Reviews D 47 (1993) 2560; I.R.C. Buckley, A. Duncan, H.F. Jones, Proof of the convergence of the linear delta expansion, Physics Reviews D 47 (1993) 2554.
16. R. Guida, K. Konishi, H. Suzuki, Convergence of scaled delta expansion: anharmonic oscillator, Annals of Physics 241 (1995) 152 [arXiv:hep-th/9407027]; R. Guida, K. Konishi, H. Suzuki, Improved convergence proof of the delta expansion and order dependent mappings, Annals of Physics 249 (1996) 109 [arXiv:hep-th/9505084]; A. Duncan, H.F. Jones, Convergence proof for optimized delta expansion: the anharmonic oscillator, Physics Reviews D 47 (1993) 2560; I.R.C. Buckley, A. Duncan, H.F. Jones, Proof of the convergence of the linear delta expansion, Physics Reviews D 47 (1993) 2554.
17. P. Amore, A. Aranda, and A. De Pace A new method for the solution of the Schrödinger equation Journal of Physics A 37 2004 3515 3525 [arXiv:quant-ph/0304043]