Solution of the Falkner–Skan equation for wedge by Adomian Decomposition Method

Alizadeh, Ebrahim; Farhadi, Mousa; Sedighi, Kurosh; Ebrahimi-Kebria, H.R.; Ghafourian, A.

doi:10.1016/j.cnsns.2007.11.002

Cited by 48 publications

(32 citation statements)

References 19 publications

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“…This method successfully and efficiently applied on some partial differential equations, which arise in applied science and physics. For example, this method applied on the several problems in science and engineering including Cauchy reaction-diffusion problems in [64], third-order dispersive partial differential equations in [65], Laplace equation [66], Fisher's equation [67], Burgers' equation [68], nonlinear Klein-Gordon with a quadratic nonlinear term in [69], Falkner-Skan for wedge [70], a system of nonlinear integro-differential equations, which arises in biology [71], degenerate parabolic equations arising in the spatial diffusion of biological population [72], Fokker-Plank equation [73], the two-dimensional parabolic partial differential equation subject to boundary integral specifications [74], Lane-Emden equation [75], delay differential equations [76] etc. For the purpose of illustration of the methodology to the ADM, we begin by considering the differential equation:…”

Section: The Adomian Decomposition Methodsmentioning

confidence: 99%

A seminumeric approach for solution of the Eikonal partial differential equation and its applications

Dehghan

Salehi

2009

Numerical Methods Partial

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In this work, a partial differential equation, which has several important applications, is investigated, and some techniques based on semianalytic (or quasi-numerical) approaches are developed to find its solution. In this article, the homotopy perturbation method (HPM), Adomian decomposition method, and the modified homotopy perturbation method are proposed to solve the Eikonal equation. HPM yields solution in convergent series form with easily computable terms, and in some case, yields exact solutions in one iteration. In other hand, in Adomian decomposition method, the approximate solution is considered as an infinite series usually converges to the accurate solution. Moreover, these methods do not require any discretization, linearization, or small perturbation, and therefore reduce the numerical computation a lot. Several test problems are given and results are compared with the variational iteration method.

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Section: The Adomian Decomposition Methodsmentioning

confidence: 99%

A seminumeric approach for solution of the Eikonal partial differential equation and its applications

Dehghan

Salehi

2009

Numerical Methods Partial

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“…Very recently, Anabtawi and Khuri [4] found numerical solutions for generalized Falkner-Skan GENERALIZED FALKNER-SKAN FLOW 699 flow of a FENE-P fluid. Alizadeh et al [5] also found the solution of the Falkner-Skan equation for wedge by utilizing Adomian decomposition method.…”

Section: Introductionmentioning

confidence: 96%

On series solution for generalized Falkner–Skan flow of a FENE‐P model

Abbasbandy¹,

Hayat²,

Maqbool³

2008

Numerical Methods in Fluids

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“…The solution of the reduced ODE was analyzed by Hartree [4]. Thereafter, ample investigations were presented regarding the Falkner-Skan flow under different aspects, few recent studies in this regard are reported in [5][6][7][8][9][10] and references therein. It is revealed that because of strong non-linearity, the previous studies were often restricted to viscous fluid and provision of numerical solutions only.…”

Section: Introductionmentioning

confidence: 99%

Hydromagnetic Falkner-Skan fluid rheology with heat transfer properties

et al. 2020

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Original scientific paper https://doi.org/10.2298/TSCI180509312A This article addresses the effects of heat transfer on magnetohydrodynamic Falkner-Skan wedge flow of a Jeffery fluid. The continuity, momentum and energy balance equations yield the relevant PDE which are transforms to ODE by exploitation of similarity variables. Strength of optimal homotopy series solutions is practiced to solved analytically the transformed ODE model of hydromagnetic Falkner-Skan fluid rheology with heat transfer scenarios. The graphical and numerical illustrations of the result are presented for different interesting flow parameters. Numerical values of Nusselt number are tabulated. It is observed that for the Falkner-Skan rheology, the applied magnetic field acts as a controlling agnet which controls the fluids velocity up to the desired value whereas Debrorah number enhances the fluid velocity.

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Solution of the Falkner–Skan equation for wedge by Adomian Decomposition Method

Cited by 48 publications

References 19 publications

A seminumeric approach for solution of the Eikonal partial differential equation and its applications

A seminumeric approach for solution of the Eikonal partial differential equation and its applications

On series solution for generalized Falkner–Skan flow of a FENE‐P model

Hydromagnetic Falkner-Skan fluid rheology with heat transfer properties

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