Application of Adomian's approximations to the Navier-Stokes equations in cylindrical coordinates

Haldar, K.

doi:10.1016/0893-9659(96)00061-4

Cited by 17 publications

(9 citation statements)

References 5 publications

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“…This technique is modified for boundary value problems with homogeneous boundary conditions. An interesting application of the decomposition approach is found in [31] where this method is applied on the Navier-Stokes equations in cylindrical coordinates. Some problems in calculus of variations are solved in [32] using the Adomian decomposition technique.…”

Section: The Decomposition Methods Of Adomianmentioning

confidence: 99%

Numerical solution of a biological population model using He’s variational iteration method

Shakeri

Dehghan

2007

Computers & Mathematics with Applications

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This paper presents numerical solution of a degenerate parabolic equation arising in the spatial diffusion of biological populations. The variational iteration method and Adomian decomposition method are used for solving this equation and then numerical results are compared with each other, showing that the variational iteration method leads to more accurate results. Furthermore, variational iteration method overcomes the difficulty arising in calculating the Adomian's polynomials which is an important advantage over the Adomian decomposition method.

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Section: The Decomposition Methods Of Adomianmentioning

confidence: 99%

Numerical solution of a biological population model using He’s variational iteration method

Shakeri

Dehghan

2007

Computers & Mathematics with Applications

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“…In 1972, Pukhnachov [24] estimated the growth rate of vorticity of axisymmetric solution of the Navier-Stokes equations under certain assumptions on the velocities. See also [20], [23], [16], [17], [22].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Properties of Axis-Symmetric D-Solutions of the Navier–Stokes Equations

Choe

Jin

2007

J. math. fluid mech.

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We consider asymptotic behavior of Leray's solution which expresses axis-symmetric incompressible Navier-Stokes flow past an axis-symmetric body. When the velocity at infinity is prescribed to be nonzero constant, Leray's solution is known to have optimum decay rate, which is in the class of physically reasonable solution. When the velocity at infinity is prescribed to be zero, the decay rate at infinity has been shown under certain restrictions such as smallness on the data. Here we find an explicit decay rate when the flow is axis-symmetric by decoupling the axial velocity and the horizontal velocities. (2000). 35Q30, 76D07. Mathematics Subject Classification

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“…For example, this method is employed on the reaction convection diffusion equation [66], Cauchy reaction-diffusion problems [67], third-order dispersive PDE in [68], Laplace equation [59], Fisher's equation [69], Burgers' equation [70], Fokker-Planck equation [71]. An interesting application of the decomposition approach is found in [72] where this method is applied on the Navier-Stokes equations in cylindrical coordinates. Some problems in calculus of variations are solved in [73] using the Adomian decomposition technique.…”

Section: The Adomian Decomposition Methods (Adm)mentioning

confidence: 99%

The use of variational iteration method and Adomian decomposition method to solve the Eikonal equation and its application in the reconstruction problem

Dehghan

Salehi

2011

Int. J. Numer. Meth. Biomed. Engng.

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SUMMARYIn this paper, the variational iteration method (VIM) and the Adomian decomposition method (ADM) are applied to solve the Eikonal equation. In addition, we apply the VIM using He's polynomials to find a semi-analytic solution of the studied model. The VIM is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. On the other hand, in the ADM the approximate solution is considered as an infinite series usually converging to the accurate solution. In addition, the results obtained using the two methods are presented. Comparison of the results reveals that the present methods are very efficient and convenient.

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Application of Adomian's approximations to the Navier-Stokes equations in cylindrical coordinates

Cited by 17 publications

References 5 publications

Numerical solution of a biological population model using He’s variational iteration method

Numerical solution of a biological population model using He’s variational iteration method

Asymptotic Properties of Axis-Symmetric D-Solutions of the Navier–Stokes Equations

The use of variational iteration method and Adomian decomposition method to solve the Eikonal equation and its application in the reconstruction problem

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