메뉴 건너뛰기




Volumn 193, Issue 2, 2007, Pages 303-310

On Linstedt-Poincaré techniques for the quintic Duffing equation

Author keywords

Artificial parameter; Galerkin method; Method of weighted residuals; Quintic Duffing equation

Indexed keywords

APPROXIMATION THEORY; GALERKIN METHODS; ORDINARY DIFFERENTIAL EQUATIONS;

EID: 35548983428     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2007.03.050     Document Type: Article
Times cited : (44)

References (34)
  • 4
    • 33645972898 scopus 로고    scopus 로고
    • Some asymptotic methods for strongly nonlinear equations
    • He Ji.-H. Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. 20 (2006) 1141-1199
    • (2006) Int. J. Mod. Phys. , vol.20 , pp. 1141-1199
    • He, Ji.-H.1
  • 5
    • 0037440579 scopus 로고    scopus 로고
    • Homotopy perturbation method: a new nonlinear analytical technique
    • He Ji.-H. Homotopy perturbation method: a new nonlinear analytical technique. Appl. Math. Comput. 135 (2003) 73-79
    • (2003) Appl. Math. Comput. , vol.135 , pp. 73-79
    • He, Ji.-H.1
  • 6
    • 33746584753 scopus 로고    scopus 로고
    • Addendum: new interpretation of homotopy perturbation method
    • He Ji.-H. Addendum: new interpretation of homotopy perturbation method. Int. J. Mod. Phys. 20 (2006) 2561-2568
    • (2006) Int. J. Mod. Phys. , vol.20 , pp. 2561-2568
    • He, Ji.-H.1
  • 7
    • 0032672778 scopus 로고    scopus 로고
    • Homotopy perturbation technique
    • He Ji.-H. Homotopy perturbation technique. Comput. Meth. Appl. Mech. Eng. 178 (1999) 257-262
    • (1999) Comput. Meth. Appl. Mech. Eng. , vol.178 , pp. 257-262
    • He, Ji.-H.1
  • 8
    • 0037412198 scopus 로고    scopus 로고
    • An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude
    • Liao S.-J. An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude. Int. J. Non-linear Mech. 38 (2003) 1173-1183
    • (2003) Int. J. Non-linear Mech. , vol.38 , pp. 1173-1183
    • Liao, S.-J.1
  • 9
  • 10
    • 0036489498 scopus 로고    scopus 로고
    • Modified Linstedt-Poincare methods for some non-linear oscillations. Part I: expansion of constant
    • He J.-H. Modified Linstedt-Poincare methods for some non-linear oscillations. Part I: expansion of constant. J. Non-linear Mech. 37 (2002) 309-314
    • (2002) J. Non-linear Mech. , vol.37 , pp. 309-314
    • He, J.-H.1
  • 11
    • 33846210009 scopus 로고    scopus 로고
    • 1/3 force by He's modified Linstedt-Poincaré method
    • 1/3 force by He's modified Linstedt-Poincaré method. J. Sound Vibr. 301 (2007) 415-419
    • (2007) J. Sound Vibr. , vol.301 , pp. 415-419
    • Öziş, T.1    Yildirim, A.2
  • 13
    • 0023648211 scopus 로고
    • Iteration procedure for determining approximate solutions to non-linear oscillator equations
    • Mickens R.E. Iteration procedure for determining approximate solutions to non-linear oscillator equations. J. Sound Vibr. 116 (1987) 185-187
    • (1987) J. Sound Vibr. , vol.116 , pp. 185-187
    • Mickens, R.E.1
  • 14
    • 33749265810 scopus 로고    scopus 로고
    • A classical iteration procedure valid for certain strongly nonlinear oscillators
    • Hu H., and Tang J.H. A classical iteration procedure valid for certain strongly nonlinear oscillators. J. Sound Vibr. 299 (2007) 397-402
    • (2007) J. Sound Vibr. , vol.299 , pp. 397-402
    • Hu, H.1    Tang, J.H.2
  • 15
    • 19944384579 scopus 로고    scopus 로고
    • A convolution integral method for certain strongly nonlinear oscillators
    • Hu H., and Tang J.H. A convolution integral method for certain strongly nonlinear oscillators. J. Sound Vibr. 285 (2005) 1235-1241
    • (2005) J. Sound Vibr. , vol.285 , pp. 1235-1241
    • Hu, H.1    Tang, J.H.2
  • 16
    • 24344480923 scopus 로고    scopus 로고
    • A generalized iteration procedure for calculating approximations to periodic solutions of "truly nonlinear oscillators"
    • Mickens R.E. A generalized iteration procedure for calculating approximations to periodic solutions of "truly nonlinear oscillators". J. Sound Vibr. 287 (2005) 1045-1051
    • (2005) J. Sound Vibr. , vol.287 , pp. 1045-1051
    • Mickens, R.E.1
  • 17
    • 0037058127 scopus 로고    scopus 로고
    • A modified Mickens procedure for certain non-linear oscillators
    • Lim C.W., and Wu B.S. A modified Mickens procedure for certain non-linear oscillators. J. Sound Vibr. 257 (2002) 202-206
    • (2002) J. Sound Vibr. , vol.257 , pp. 202-206
    • Lim, C.W.1    Wu, B.S.2
  • 18
    • 33644600306 scopus 로고    scopus 로고
    • 1/3 force oscillators
    • 1/3 force oscillators. J. Sound Vibr. 292 (2006) 964-968
    • (2006) J. Sound Vibr. , vol.292 , pp. 964-968
    • Mickens, R.E.1
  • 19
    • 33646517251 scopus 로고    scopus 로고
    • Solutions of nonlinear oscillators with fractional powers by an iterative procedure
    • Hu H. Solutions of nonlinear oscillators with fractional powers by an iterative procedure. J. Sound Vibr. 294 (2006) 608-614
    • (2006) J. Sound Vibr. , vol.294 , pp. 608-614
    • Hu, H.1
  • 20
    • 33745664224 scopus 로고    scopus 로고
    • A modified iteration perturbation method for some nonlinear oscillation problems
    • Marinca V., and Herinasu N. A modified iteration perturbation method for some nonlinear oscillation problems. Acta Mech. 184 (2006) 142-231
    • (2006) Acta Mech. , vol.184 , pp. 142-231
    • Marinca, V.1    Herinasu, N.2
  • 21
    • 33748424980 scopus 로고    scopus 로고
    • An analytical approximate technique for a class of strongly non-linear oscillators
    • Wu B.S., Sun W.P., and Lim C.W. An analytical approximate technique for a class of strongly non-linear oscillators. Int. J. Non-linear Mech. 41 (2006) 766-774
    • (2006) Int. J. Non-linear Mech. , vol.41 , pp. 766-774
    • Wu, B.S.1    Sun, W.P.2    Lim, C.W.3
  • 22
    • 0037412162 scopus 로고    scopus 로고
    • Analytical approximation to large-amplitude oscillation of a non-linear conservative system
    • Wu B.S., Lim C.W., and Ma Y.F. Analytical approximation to large-amplitude oscillation of a non-linear conservative system. Int. J. Non-linear Mech. 38 (2003) 1037-1043
    • (2003) Int. J. Non-linear Mech. , vol.38 , pp. 1037-1043
    • Wu, B.S.1    Lim, C.W.2    Ma, Y.F.3
  • 23
    • 0141882931 scopus 로고    scopus 로고
    • Large amplitude non-linear oscillations of a general conservative system
    • Wu B.S., and Lim C.W. Large amplitude non-linear oscillations of a general conservative system. Int. J. Non-linear Mech. 39 (2004) 859-870
    • (2004) Int. J. Non-linear Mech. , vol.39 , pp. 859-870
    • Wu, B.S.1    Lim, C.W.2
  • 24
    • 0035686567 scopus 로고    scopus 로고
    • A method for obtaining approximate analytic periods for a class of nonlinear oscillators
    • Wu B., and Li P. A method for obtaining approximate analytic periods for a class of nonlinear oscillators. Meccanica 36 (2001) 167-176
    • (2001) Meccanica , vol.36 , pp. 167-176
    • Wu, B.1    Li, P.2
  • 25
    • 15944389556 scopus 로고    scopus 로고
    • Improved Linstedt-Poicaré method for the solution of nonlinear problems
    • Amore P., and Aranda A. Improved Linstedt-Poicaré method for the solution of nonlinear problems. J. Sound Vibr. 283 (2005) 1115-1136
    • (2005) J. Sound Vibr. , vol.283 , pp. 1115-1136
    • Amore, P.1    Aranda, A.2
  • 26
    • 2942571550 scopus 로고    scopus 로고
    • High order analysis of nonlinear periodic differential equations
    • Amore P., and Lamas H.M. High order analysis of nonlinear periodic differential equations. Phys. Lett. A 327 (2004) 158-166
    • (2004) Phys. Lett. A , vol.327 , pp. 158-166
    • Amore, P.1    Lamas, H.M.2
  • 27
    • 1642616365 scopus 로고    scopus 로고
    • Presenting a new method for the solution of nonlinear problems
    • Amore P., and Aranda A. Presenting a new method for the solution of nonlinear problems. Phys. Lett. A 316 (2003) 218-225
    • (2003) Phys. Lett. A , vol.316 , pp. 218-225
    • Amore, P.1    Aranda, A.2
  • 28
    • 33751567742 scopus 로고    scopus 로고
    • Development of accurate solutions for a classical oscillator
    • Amore P., and Sanchez N.E. Development of accurate solutions for a classical oscillator. J. Sound Vibr. 283 (2007) 345-351
    • (2007) J. Sound Vibr. , vol.283 , pp. 345-351
    • Amore, P.1    Sanchez, N.E.2
  • 29
    • 19444376778 scopus 로고    scopus 로고
    • Comparison of alternative improved perturbative methods for nonlinear oscillations
    • Amore P., Raya A., and Fernández F.M. Comparison of alternative improved perturbative methods for nonlinear oscillations. Phys. Lett. A 340 (2005) 201-208
    • (2005) Phys. Lett. A , vol.340 , pp. 201-208
    • Amore, P.1    Raya, A.2    Fernández, F.M.3
  • 30
    • 0038394235 scopus 로고    scopus 로고
    • High-order variational calculation for the frequency of time-periodic solutions
    • Pelster A., Kleinert H., and Schanz M. High-order variational calculation for the frequency of time-periodic solutions. Phys. Rev. E 67 (2003) 016604-1/6
    • (2003) Phys. Rev. E , vol.67
    • Pelster, A.1    Kleinert, H.2    Schanz, M.3
  • 31
    • 0027911989 scopus 로고
    • A perturbation technique that works even when the non-linearity is not small
    • Senator M., and Bapat C.N. A perturbation technique that works even when the non-linearity is not small. J. Sound Vibr. 164 (1993) 1-27
    • (1993) J. Sound Vibr. , vol.164 , pp. 1-27
    • Senator, M.1    Bapat, C.N.2
  • 32
    • 20444380770 scopus 로고    scopus 로고
    • A generalization of the Senator-Bapat method for certain strongly nonlinear oscillators
    • Wu B.S., Lim C.W., and Li P.S. A generalization of the Senator-Bapat method for certain strongly nonlinear oscillators. Phys. Lett. A 341 (2005) 164-169
    • (2005) Phys. Lett. A , vol.341 , pp. 164-169
    • Wu, B.S.1    Lim, C.W.2    Li, P.S.3
  • 33
    • 0025887981 scopus 로고
    • A modified Linstedt-Poincaré method for certain strongly non-linear oscillators
    • Cheung Y.K., Chen S.H., and Lau S.L. A modified Linstedt-Poincaré method for certain strongly non-linear oscillators. Int. J. Non-linear Mech. 26 (1991) 367-378
    • (1991) Int. J. Non-linear Mech. , vol.26 , pp. 367-378
    • Cheung, Y.K.1    Chen, S.H.2    Lau, S.L.3
  • 34
    • 4644353662 scopus 로고    scopus 로고
    • Comparison of two Linstedt-Poincaré-type perturbation methods
    • Hu H., and Xiong Z.G. Comparison of two Linstedt-Poincaré-type perturbation methods. J. Sound Vibr. 278 (2004) 437-444
    • (2004) J. Sound Vibr. , vol.278 , pp. 437-444
    • Hu, H.1    Xiong, Z.G.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.