Reconstruction of Variational Iteration Algorithms using the Laplace Transform

Hesameddini, Esmail; Latifizadeh, Habibolla

doi:10.1515/ijnsns.2009.10.11-12.1377

Cited by 71 publications

(44 citation statements)

References 16 publications

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“…We apply Laplace transform to identify the Lagrange multiplier [42][43][44]. By using Laplace transform, we have…”

Section: Basic Concept Of Vim-iimentioning

confidence: 99%

Assesment of New Analytical Method for Solving the Foam Drainage Equation

Nikkar

2014

Chinese Journal of Mathematics

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The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. In this study, a new reliable technique is used to handle the foam drainage equation. This new method resulted from VIM by a simple modification, that is, variational iteration method-II (VIM-II). It has been shown that the VIM-II is a powerful technique in obtaining accurate solutions that cannot be given otherwise by perturbation and other methods. The accuracy and convergence of the method are also investigated and compared with other methods. The results showed that there are good agreements between the results.

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“…We apply Laplace transform to identify the Lagrange multiplier [42][43][44]. By using Laplace transform, we have…”

Section: Basic Concept Of Vim-iimentioning

confidence: 99%

Assesment of New Analytical Method for Solving the Foam Drainage Equation

Nikkar

2014

Chinese Journal of Mathematics

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“…In recent years many authors have paid attention to studying the solutions of linear and nonlinear partial differential equations by using various methods. Among these are the Adomian decomposition method (ADM) [8], Hes semi-inverse method [9], the tanh method, the homotopy perturbation method (HPM), the sinhcosh method, the differential transform method and the variational iteration method (VIM) [10,11,12,13,14,15,16,17,18,19]. Most of these methods have their inbuilt deficiencies like the calculation of Adomians polynomials, the Lagrange multiplier, divergent results and huge computational work.…”

Section: Introductionmentioning

confidence: 99%

The Combined Laplace-homotopy Analysis Method for Partial Differential Equations

Vahidi¹

2017

J. Math. Computer Sci.

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In this paper, the Laplace transform homotopy analysis method (LHAM) is employed to obtain approximate analytical solutions of the linear and nonlinear differential equations. This method is a combined form of the Laplace transform method and the homotopy analysis method. The proposed scheme finds the solutions without any discretization or restrictive assumptions and is free from round-off errors and therefore, reduces the numerical computations to a great extent. Some illustrative examples are presented and the numerical results show that the solutions of the LHAM are in good agreement with those obtained by exact solution.

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“…It has been caught much attention since 2007 [3,4], when the method was systematically summarized and variational iteration formulae for various nonlinear equations were given. See, for examples, Eqs.…”

Section: Introductionmentioning

confidence: 99%

“…(18d)-(25d) in Ref. [4]. The method became accessible to non mathematicians and it is reviewed, with applications, in Refs.…”

Section: Introductionmentioning

confidence: 99%