The use of He's variational iteration method for solving variational problems

References

• Abbasbandy , S. 2007 . A new application of He's variational iteration method for quadratic Riccati differential equation by using Adomian's polynomials . J. Comput. Appl. Math , 207 : 59 – 63 .
   Web of Science ®Google Scholar
• Abdulaziz , Q. , Hashim , I. and Chowdhury , M. S.H. 2008 . Solving variational problems by homotopy-perturbation method . Int. J. Numer. Methods Eng. , 175 : 709 – 721 .
   Google Scholar
• Chang , R. Y. and Wang , M. L. 1983 . Shifted Legendre direct method for variational problems . J. Optimi. Theory Appl. , 39 : 299 – 307 .
   Web of Science ®Google Scholar
• Chen , C. F. and Hsiao , C. H. 1975 . A Walsh series direct method for solving variational problems . J. Franklin Instit. , 300 : 265 – 280 .
   Web of Science ®Google Scholar
• Dehghan , M. and Saadatmandi , A. 2008 . A Variational iteration method for solving the wave equation subject to an integral conservation condition . Chaos Solitons and Fractals , in press
   Google Scholar
• Dehghan , M. and Shakeri , F. 2007 . Numerical solution of a biological population model using He's variational iteration method . Comput. Math. Appl. , 54 : 1197 – 1209 .
   Web of Science ®Google Scholar
• Dehghan , M. and Shakeri , F. 2008 . Approximate solution of a differential equation arising in astrophysics using the variational iteration method . New Astronomy , 13 : 53 – 59 .
   Web of Science ®Google Scholar
• Dehghan , M. and Shakeri , F. 2008 . Application of He's variational iteration method for solving the Cauchy reaction-diffusion problem . J. Comput. Appl. Math. , 214 : 435 – 446 .
   Web of Science ®Google Scholar
• Dehghan , M. and Shakeri , F. 2008 . Solution of parabolic integro–differential equations arising in heat conduction in materials with memory via He's variational iteration technique . Comm. Numer. Methods Engrg , in press
   PubMedGoogle Scholar
• Dehghan , M. and Tatari , M. 2006 . The use of Adomian decomposition method for solving problems in calculus of variation . Math. Prob. Eng. , 2006 : 1 – 12 .
   Web of Science ®Google Scholar
• Dehghan , M. and Tatari , M. 2006 . The use of He's variational iteration method for solving a Fokker–Planck equation . Phys. Scr. , 74 : 310 – 316 .
   Web of Science ®Google Scholar
• Dehghan , M. and Tatari , M. 2008 . Identifying an unknown function in a parabolic equation with overspecified data via He's variational iteration method . Chaos, Solitons and Fractals , 36 : 157 – 166 .
   Web of Science ®Google Scholar
• Elgolic , L. E. 1962 . Calculus of Variations , Oxford : Pergamon press .
   Google Scholar
• Elsgolts , L. 1977 . Differential Equations and the Calculus of Variations , Moscow : Mir Publisher . translated from the Russian by G. Yankovsky
   Google Scholar
• Finlayson , B. A. 1972 . The Method of Weighted Residuals and Variational Principles , New York : Academic Press .
   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 : 35 – 45 .
   Web of Science ®Google Scholar
• Gelfand , I. M. and Fomin , S. V. 1963 . Calculus of Variations , Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Glabisz , W. 2004 . Direct Walsh-wavelet packet method for variational problems . Appl. Math. Comput. , 159 : 769 – 781 .
   Google Scholar
• He , J.-H. 1997 . A new approach to non-linear partial differential equations . Commun. Non-Linear Sci. Numer. Simul. , 2 ( 4 ) : 230 – 235 .
   Google Scholar
• He , J.-H. 1999 . Variational iteration method – a kind of non-linear analytical technique: some examples . Int. J. Non-Linear Mech. , 34 : 699 – 708 .
   Web of Science ®Google Scholar
• He , J.-H. 2004 . Variational principles for some nonlinear partial equations with variable coefficients . Chaos, Solitons and Fractals , 19 : 847 – 851 .
   Web of Science ®Google Scholar
• He , J.-H. 2006 . Some asymptotic methods for strongly nonlinear equations . Int. J. Modern Phys. B , 20 ( 10 ) : 1141 – 1199 .
   Web of Science ®Google Scholar
• He , J.-H. 2006 . Non-perturbative methods for strongly nonlinear problems , Berlin : de-Verlag in internet, GmbH . dissertation
   Google Scholar
• Horng , I. R. and Chou , J. H. 1985 . Shifted Chebyshev direct method for solving variational problems . Int. J. Syst. Sci. , 16 : 855 – 861 .
   Web of Science ®Google Scholar
• Hsiao , C. H. 2004 . Haar wavelet direct method for solving variational problems . Math. Comput. Simul. , 64 : 569 – 585 .
   Web of Science ®Google Scholar
• Hwang , C. and Shih , Y. P. 1983 . Laguerre series direct method for variational problems . J. Optim. Theory Appl. , 39 : 143 – 149 .
   Web of Science ®Google Scholar
• Inokuti , M. 1978 . “ General use of the Lagrange multiplier in non-linear mathematical physics ” . In Variational Method in the Mechanics of Solids , Edited by: Nemat-Nasser , S. 156 – 162 . Oxford : Pergamon Press .
   Google Scholar
• Krasnov , M. L. , Makarenko , G. I. and Kiselev , A. I. 1975 . Problems and Exercises in the Calculus of Variations , Moscow : MIR Publishers . translated from the Russian by G. Yankovsky
   Google Scholar
• Razzaghi , M. and Ordokhani , Y. 2001 . An application of rationalized Haar functions for variational problems . Appl. Math. Comput. , 122 : 353 – 364 .
   Web of Science ®Google Scholar
• Razzaghi , M. and Razzaghi , M. 1988 . Fourier series direct method for variational problems . Int. J. Control , 48 : 887 – 895 .
   Web of Science ®Google Scholar
• Razzaghi , M. and Yousefi , S. 2000 . Legendre wavelets direct method for variational problems . Math. Comput. Simul. , 53 : 185 – 192 .
   Web of Science ®Google Scholar
• Shakeri , F. and Dehghan , M. 2008 . Numerical solution of the Klein–Gordon equation via He's variational iteration method . Nonlinear Dyn. , 51 : 89 – 97 .
   Web of Science ®Google Scholar
• Shakeri , F. and Dehghan , M. 2008 . Solution of a model describing biological species living together using the variational iteration method . Math. Comput. Model. , 148 : 686 – 699 .
   Google Scholar
• Shou , D.-H. and He , J.-H. 2008 . Beyond Adomian method: the variational iteration method for solving heat-like and wave-like equations with variable coefficients . Phys. Lett. A , 372 : 233 – 237 .
   Web of Science ®Google Scholar
• Sweilam , N. H. and Khader , M. M. 2007 . Variational iteration method for one dimensional non-linear thermoelasticity . Chaos, Solitons and Fractals , 32 : 145 – 149 .
   Web of Science ®Google Scholar
• Tatari , M. and Dehghan , M. 2007 . On the convergence of He's variational iteration method . J. Comput. Appl. Math. , 207 : 121 – 128 .
   Web of Science ®Google Scholar
• Tatari , M. and Dehghan , M. 2007 . Solution of problems in calculus of variations via He's variational iteration method . Phys. Lett. A , 362 : 401 – 406 .
   Web of Science ®Google Scholar
• Tikhomirov , V. M. 1990 . Store about Maxima and Minima , Providence, RI : American Mathematica Society .
   Google Scholar
• Wazwaz , A. M. 2007 . A comparison between the variational iteration method and Adomian decomposition method . J. Comput. Appl. Math. , 207 : 129 – 136 .
   Web of Science ®Google Scholar
• Wazwaz , A. M. 2007 . The variational iteration method for a reliable treatment of the linear and the nonlinear Goursat problem . Appl. Math. Comput. , 193 : 455 – 462 .
   Web of Science ®Google Scholar
• Xu , L. 2007 . Variational iteration method for solving integral equations . Comput. Math. Appl. , 54 : 1071 – 1078 .
   Google Scholar