Variational iteration method for fractional heat- and wave-like equations

R, Yulita Molliq; Noorani, Mohd Salmi Md; Hashim, Ishak

doi:10.1016/j.nonrwa.2008.02.026

Cited by 151 publications

(94 citation statements)

References 39 publications

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“…and its closed form solutions at various values of α becomes u(x 1 , x 2 , x 3 ,t) = x which are the same as the solutions obtained by other methods [14,19]. Though the solution series in each example converges to the exact closed form analytic solution of the problem, we show that only few terms of the solution series (21) are required to give a quite accurate solution.…”

Section: Example 51 Consider the Following N-dimensional Heat-like supporting

confidence: 71%

“…, respectively, for n = 4, which is the same as the solution obtained by other methods [14,19]. Example 5.3.…”

Section: Example 51 Consider the Following N-dimensional Heat-like supporting

confidence: 58%

“…Taking n = 3, c 1 = c 2 = 2π, and γ = 1 in (23) and (27), we obtain the analytical solution of [14,19].…”

Section: Example 51 Consider the Following N-dimensional Heat-like mentioning

confidence: 99%

“…The fractional wavelike equation can be used to describe different models in anomalous diffusive and sub diffusive systems, description of fractional random walk, unification of diffusion and wave propagation phenomenon [15 -18]. Several authors [14,19,20] applied the Adomian decomposition method (ADM), the variational iteration method (VIM), and the homotopy analysis method (HAM) successfully to solve two-and threedimensional fractional heat-and wave-like equations.…”

Section: Introductionmentioning

confidence: 99%

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Analytic Solution of Fractional-Order Heat- and Wave-Like Equations Using Generalized n-dimensional Differential Transform Method

Baranwal

Pandey

Tripathi

et al. 2011

Zeitschrift Für Naturforschung A

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In this paper, we have introduced a generalized n-dimensional differential transform method to propose a user friendly algorithm to obtain the closed form analytic solution for n-dimensional fractional heat-and wave-like equations. Three examples are given to establish the simplicity of the algorithm. In Example 5.3, we show that ten terms of the series representing the solution, even in fractional order, give a very accurate solution.

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Section: Example 51 Consider the Following N-dimensional Heat-like supporting

confidence: 71%

“…, respectively, for n = 4, which is the same as the solution obtained by other methods [14,19]. Example 5.3.…”

Section: Example 51 Consider the Following N-dimensional Heat-like supporting

confidence: 58%

“…Taking n = 3, c 1 = c 2 = 2π, and γ = 1 in (23) and (27), we obtain the analytical solution of [14,19].…”

Section: Example 51 Consider the Following N-dimensional Heat-like mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Analytic Solution of Fractional-Order Heat- and Wave-Like Equations Using Generalized n-dimensional Differential Transform Method

Baranwal

Pandey

Tripathi

et al. 2011

Zeitschrift Für Naturforschung A

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“…While the VIM [15] requires the determination of Lagrange multiplier in its computational algorithm, DJM is independent of any such requirements. Moreover, unlike the ADM [16], where the cal-culation of the tedious Adomian polynomials is needed to deal with nonlienar terms, DJM handles linear and nonlinear terms in a simple and straightforward manner without any additional requirements.…”

Section: U Y Z T F Y Z T U a Y Z T F Y Z T U X Z T G X Z T U X B Z T mentioning

confidence: 99%

Daftardar-Jafari Method for Fractional Heat-Like and Wave-Like Equations with Variable Coefficients

Al-Hayani¹

2017

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Application of the variational iteration method to nonlinear non‐Fourier conduction heat transfer equation with variable coefficient

Saedodin

Yaghoobi

Torabi

2011

Heat Trans. Asian Res.

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In this paper, a variational iteration method (VIM) has been applied to nonlinear non-Fourier conduction heat transfer equation with variable specific heat coefficient. The concept of the variational iteration method is introduced briefly for applying this method for problem solving. The proposed iterative scheme finds the solution without any discretization, linearization, or restrictive assumptions. The results of VIM as an analytical solution are then compared with those derived from the established numerical solution obtained by the fourth order Runge-Kutta method in order to verify the accuracy of the proposed method. The results reveal that the VIM is very effective and convenient in predicting the solution of such problems, and it is predicted that VIM can find a wide application in new engineering problems.

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Variational iteration method for fractional heat- and wave-like equations

Cited by 151 publications

References 39 publications

Analytic Solution of Fractional-Order Heat- and Wave-Like Equations Using Generalized n-dimensional Differential Transform Method

Analytic Solution of Fractional-Order Heat- and Wave-Like Equations Using Generalized n-dimensional Differential Transform Method

Daftardar-Jafari Method for Fractional Heat-Like and Wave-Like Equations with Variable Coefficients

Application of the variational iteration method to nonlinear non‐Fourier conduction heat transfer equation with variable coefficient

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