Solution of Blasius Equation by Variational Iteration

Liu, Yucheng; Kurra, Sree N.

doi:10.5923/j.am.20110101.03

Cited by 14 publications

(10 citation statements)

References 22 publications

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“…Those comparisons point out that the VIM may be considered as an efficient alternative method for solving a wide range of physical nonlinear problems, especially those arising in the area of fluid dynamics. We point out how the VIM can also be applied to any heat transfer and flow problem leading to a coupled nonlinear system of ODEs, see for instance [5,14,16,17,23,31,35] without any claim to completeness. The major advantage of the VIM, unlike the common numerical methods, is of providing analytical approximation or an approximated solution without linearization, perturbation, closure approximation, or discretization.…”

Section: Discussionmentioning

confidence: 99%

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Approximate Analytical Solution of a Third-Order IVP arising in Thin Film Flows driven by Surface Tension

Morlando

2017

B Soc Paran Mat

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In this paper, we present a way of applying the so-called He's variational iteration method (VIM) to numerically solve the non linear autonomous third-order ordinary differential equation (ODE) y ′′′ = y −2 obtained by considering a traveling wave solution admitted by a lubrication equation modeling a twodimensional spreading of a thin viscous film on a inclined slope. Approximate analytical solution is derived and compared to the results obtained from the Adomian decomposition method (ADM) proposed in [20], to the exact analytical solution [7,8], to a fifth order Runge-Kutta method (DOPRI), a fourth order Runge-Kutta method (RK4), a three-stage fifth order Runge-Kutta method (RKD5) developed in [18]. A very good agreement and accuracy is observed. Comparisons are obtained using symbolic capabilities of Maple 18.0 package.

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Section: Discussionmentioning

confidence: 99%

“…Here we point out that just the first approximation y1 is capable to be an efficient approximation of the exact solution as is the case of the Blasius equation, see [17].…”

Section: Application Of Vimmentioning

confidence: 99%

Approximate Analytical Solution of a Third-Order IVP arising in Thin Film Flows driven by Surface Tension

Morlando

2017

B Soc Paran Mat

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“…, which is easily seen to have the theoretical solution u(x, t) = x 2 /2 + t. Using Eqn. (19) by assuming u 0 (x, t) = f(x) = x 2 /2, and other components can be obtained using the functional formula as:…”

Section: Examplementioning

confidence: 99%

“…Besides the aforementioned numerical methods, HVIM is an effective and convenient method for solving both weakly and strongly nonlinear equations, which was originally presented by He for solving differential equation systems [10][11][12][13]. The author has extensively applied HVIM for solving broad types of differential equation systems, such as heat equations, free vibration of Euler-Bernoulli beam, the nonlinear differential difference equations, Blasius equations, and [16][17][18][19]. From those works, it is found that both HVIM and ADM are efficient and powerful methods which can lead to correct solutions in closed form.…”

Section: Introductionmentioning

confidence: 99%

The use of He's variational iteration method for solving the one-dimensional parabolic equation with non-classical boundary conditions

Liu

Chand

2013

ams

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Over the last 15 years, the He's variational iteration method (HVIM) has been applied to obtain formal solutions to a wide class of differential equations. This method leads to computable, efficient, solutions to linear and nonlinear operator equations. The parabolic partial differential equations with non-classical boundary conditions model various physical problems. The aim of this paper is to investigate the application of HVIM for solving the second-order linear parabolic partial differential equation with non-classical boundary conditions. The HVIM provides a reliable technique that requires less work when compared with the traditional techniques such as the Adomian decomposition method (ADM). The present approach can be used and extended for investigating more scientific applications.

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“…The accurate solution of Blasius equation has been obtained by numerical integration [1] and other numerical methods [3,4]. However, this fluid problem derived by the Blasius equation has been solved by various analytical methods [5,6].…”

Section: Fig 1: Velocity Boundary Layer Development On a Flat Plate [2]mentioning

confidence: 99%

Boundary-Layer Theory of Fluid Flow past a Flat-Plate: Numerical Solution using MATLAB

Bani-Hani¹,

Assad²

2018

IJCA

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Fluid mechanics may have complicated systems where the analytical solution is tedious and time consuming. Changing one or more boundary conditions may add more challenges. Computer software provides easy and flexible solution to the fluid mechanics systems even when the boundary conditions are changing to describe the reality. In this work MATLAB code is used to solve the well-known third order ordinary differential equation that is Blasius equation. The results obtained are compared to other numerical and analytical solution available in the literature.Results showed that with a simple code written using MATLAB the problem can be simulated and solved easily. A comparison between the solution obtained by MATLAB and the solutions published in literature showed a comparable results and same trends. Computers software allows getting very accurate results depending on the numerical method selected for the solution.

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Solution of Blasius Equation by Variational Iteration

Cited by 14 publications

References 22 publications

Approximate Analytical Solution of a Third-Order IVP arising in Thin Film Flows driven by Surface Tension

Approximate Analytical Solution of a Third-Order IVP arising in Thin Film Flows driven by Surface Tension

The use of He's variational iteration method for solving the one-dimensional parabolic equation with non-classical boundary conditions

Boundary-Layer Theory of Fluid Flow past a Flat-Plate: Numerical Solution using MATLAB

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