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Application of the variational iteration method to some nonlinear one-dimensional oscillations. (English) Zbl 1238.70018
From the introduction: In this paper a kind of analytical technique for a general nonlinear problem is presented. The problems are initially approximated with unknown constants, which can be further determined. The iterative process is constructed by a general Lagrange multiplier, which can be identified optimally via variational theory. This method is effective and accurate for nonlinear problems with approximations converging rapidly to accurate solutions.
MSC:
70K40Forced nonlinear motions (general mechanics)
70-08Computational methods (mechanics of particles and systems)
References:
[1]He J-H (2000) A modified perturbation technique depending upon an artificial parameter. Meccanica 35(4):299–311 · Zbl 0986.70016 · doi:10.1023/A:1010349221054
[2]He J-H (1999) Variational iteration method–a kind of non-linear analytical technique: some examples. Int J Non-Linear Mech 34(4):699–708 · Zbl 05137891 · doi:10.1016/S0020-7462(98)00048-1
[3]Marinca V (2002) An approximate solution for one-dimensional weakly nonlinear oscillations. Int J Nonlinear Sci Num Sim 3:107–120
[4]Gradshteyn IS, Ryzhik IM (1980) Tables of integrals, series and products. Academic Press, New York
[5]Nayfeh AH, Mook DT (1979) Nonlinear oscillations. Willey, New York
[6]He JH (2007) Variational iteration method. Some recent results and new interpretations. J Comp Appl Math 207(1):3–17 · Zbl 1119.65049 · doi:10.1016/j.cam.2006.07.009
[7]Wu B, Li P (2001) A method for obtaining approximate analytic periods for a class of nonlinear oscillators. Meccanica 36(2):167–176 · Zbl 1008.70016 · doi:10.1023/A:1013067311749
[8]Spanos PD, Di Paola M, Failla G (2001) A Galerkin approach for power spectrum determination of nonlinear oscillators. Meccanica 37(1–2):51–65 · Zbl 1060.70031 · doi:10.1023/A:1019610512675
[9]Marinca V, Herişanu N (2006) Periodic solutions of Duffing equation with strong nonlinearity. Chaos Solitons Fractals (2006, in press). doi: 10.1016/j.chaos.2006.08.033