Application of He's homotopy perturbation and He's variational iteration methods for solution of Benney–Lin equation

References

• Ariel , P. D. , Hayat , T. and Asghar , S. 2006 . Homotopy perturbation method and axisymmteric flow over a stretching sheet . Int. J. Nonlinear Sci. Numer. Simul. , 7 ( 4 ) : 399
   Google Scholar
• Benney , D. J. 1966 . Long waves on liquid films . J. Math. Phys. , 45 : 150
   Web of Science ®Google Scholar
• Berloff , N. G. and Howard , L. N. 1997 . Solitary and periodic solutions of nonlinear nonintegrable equations . Stud. Appl. Math. , 99 : 1
   Google Scholar
• Chen , W. and Li , J. 2008 . On the low regularity of the Benney–Lin equation . J. Math. Anal. Appl. , 339 : 1134
   Google Scholar
• Ganji , D. D. 2006 . The application of He's homotopy perturbation method to nonlinear equation arising in heat transfer . Phys. Lett. A , 355 : 337
   Web of Science ®Google Scholar
• Ganji , D. D. and Hashemi , S. H. 2007 . Explicit solution for fourth-order equations with variable coefficients in higher-dimensional spaces using He's homotopy perturbation method . Far East J. Appl. Math. , 26 ( 3 ) : 305
   Google Scholar
• Ganji , D. D. and Rafei , M. 2006 . Explicit solutions of Helmholtz equation and fifth-order KDV equation using homotopy perturbation method . Int. J. Non-linear Sci. Numer. Simul. , 7 ( 3 ) : 321
   Google Scholar
• Ganji , D. D. and Rajabi , A. 2006 . Assessment of homotopy–perturbation and perturbation methods in heat radiation equations . Int. Commun. Heat Mass Transf. , 33 ( 3 ) : 391
   Web of Science ®Google Scholar
• Ganji , D. D. and Sadighi , A. 2006 . Application of He's homotopy-perturbation method to nonlinear coupled systems of reaction-diffused equations . Int. J. Non-linear Sci. Numer. Simul. , 7 ( 4 ) : 411
   Web of Science ®Google Scholar
• Ganji , D. D. and Sadighi , A. 2007 . Application of homotopy-perturbation and variational iteration methods to nonlinear heat transfer and porous media equations . J. Comput. Appl. Math. , 207 ( 1 ) : 24
   Web of Science ®Google Scholar
• Ganji , D. D. , Jannatabadi , M. and Mohseni , E. 2007 . Application of He's variational iteration method to nonlinear Jaulent-Miodek equations and comparing it with ADM . J. Comput. Appl. Math. , 207 ( 1 ) : 35
   Web of Science ®Google Scholar
• He , J. H. 1997 . A new approach to nonlinear partial differential equations . Commun. Nonlinear Sci. Numer. Simul. , 2 ( 4 ) : 230
   Google Scholar
• He , J. H. 1998 . Approximate analytical solution for seepage flow with fractional derivatives in porous media . Comput. Methods Appl. Mech. Eng. , 167 : 57
   Web of Science ®Google Scholar
• He , J. H. 1998 . Approximate solution of nonlinear differential equations with convolution product nonlinearities . Comput. Methods Appl. Mech. Eng. , 167 : 69
   Web of Science ®Google Scholar
• He , J. H. 1999 . Homotopy perturbation technique . J. Comput. Methods Appl. Mech. Eng. , 178 ( 3–4 ) : 257
   Web of Science ®Google Scholar
• He , J. H. 1999 . Variational iteration method – a kind of nonlinear analytical technique: some examples . Int. J. Nonlinear Mech. , 34 : 699
   Web of Science ®Google Scholar
• He , J. H. 2000 . A coupling method of a homotopy technique and a perturbation technique for non-linear problems . Int. J. Non-linear Mech. , 35 : 37
   Web of Science ®Google Scholar
• He , J. H. 2000 . Variational iteration method for autonomous ordinary differential systems . Appl. Math. Comput. , 114 ( 2/3 ) : 115
   Web of Science ®Google Scholar
• He , J. H. 2005 . Limit cycle and bifurcation of nonlinear problems . Chaos Solitons Fractals , 26 ( 3 ) : 827
   Web of Science ®Google Scholar
• He , J. H. 2005 . Asymptotology by homotopy perturbation method . Int. J. Nonlinear Sci. Numer. Simul. , 6 ( 2 ) : 207
   Web of Science ®Google Scholar
• He , J. H. 2005 . A generalized variational principle in micromorphic thermoelasticity . Mech. Res. Commun. , 3291 : 93
   Google Scholar
• He , J. H. 2005 . Application of homotopy perturbation method to nonlinear wave equations . Chaos Solitons Fractals , 26 : 695
   Web of Science ®Google Scholar
• He , J. H. 2006 . Some asymptotic methods for strongly nonlinear equations . Int. J. Mod. Phys. B , 20 ( 10 ) : 1141
   Web of Science ®Google Scholar
• He , J. H. and Wu , X. H. 2006 . Construction of solitary solution and compacton-like solution by variational iteration method . Chaos Solitons Fractals , 29 ( 1 ) : 108
   Web of Science ®Google Scholar
• He , J. H. 2006 . Homotopy perturbation method for solving boundary value problems . Phys. Lett. A , 350 ( 1–2 ) : 87
   Web of Science ®Google Scholar
• Lin , S. P. 1974 . Finite amplitude side-band stability of a viscous film . J. Fluid Mech. , 63 : 417
   Web of Science ®Google Scholar
• Rafei , M. , Ganji , D. D. , Mohammadi Daniali , H. R. and Pashaei , H. 2007 . Application of homotopy perturbation method to the RLW and generalized modified Boussinesq equations . Phys. Lett. A , 364 : 1
   Web of Science ®Google Scholar
• Sepulveda , M. and Vera , O. 2007 . Numerical method for the KdV–Kawahara and Benney–Lin equations . Proc. Appl. Math. Mech. , 7 DOI: 10.1002/pamm.200700192
   Google Scholar
• Tari , H. , Ganji , D. D. and Babazadeh , H. 2007 . The application of He's variational iteration method to nonlinear equations arising in heat transfer . Phys. Lett. A , 363 ( 3 ) : 213
   Google Scholar