Solutions of time-dependent Emden–Fowler type equations by homotopy analysis method

Bataineh, A. Sami; Noorani, Mohd Salmi Md; Hashim, Ishak

doi:10.1016/j.physleta.2007.05.094

Cited by 97 publications

(57 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Homotopy perturbation method (HPM) solution is a special case of Homotopy analysis method (HAM) solution whenh = −1. This fact has been pointed out by many researchers such as Abbasbandy [20], Liao et al [16], Bataineh et al [21], Van Gorder et al [22], Hayat and Sajid [23], Turkyilmazoglu [24], Das and Gupta [25]. A comparison between the absolute error for HAM (h = −1.09), HPM and the exact solution at t = 1 and various values of x is presented in Table 1.…”

Section: Numerical Examplesmentioning

confidence: 64%

Approximate Solution of an Unknown Coefficients in Parabolic Equation

Bayrak¹,

Can²

2014

Appl. Math. Inf. Sci.

View full text Add to dashboard Cite

Abstract:In this paper, an inverse parabolic equation is solved by using the homotopy analysis method (HAM) and the homotopy perturbation method (HPM). The approximation solution of this equation is calculated in the form of series which its components are computed easily. HPM is shown not always to generate a continuous family of solutions in terms of the homotopy parameter. By the convergence-control parameter this can however be prevented to occur in the HAM. Illustrative examples are presented to exhibit a comparison between the HAM and the HPM.

show abstract

Section: Numerical Examplesmentioning

confidence: 64%

Approximate Solution of an Unknown Coefficients in Parabolic Equation

Bayrak¹,

Can²

2014

Appl. Math. Inf. Sci.

View full text Add to dashboard Cite

show abstract

“…Some researchers dealed with this type of models [1][2][3][4][5][6][7][8][9]. These physical models describe some important equations as the Navier-Stokes equations can be converted into various heat-like equation in some special cases [10].…”

Section: Conditions U(0 T) = V(t) and U X (0 T) = 0 Where G(x T)ymentioning

confidence: 99%

Non-Polynomial Spline Method for a Time-Dependent Heat-Like Lane- Emden Equation

Çağlar

Uçar

2012

Acta Phys. Pol. A

View full text Add to dashboard Cite

In this study, a time-dependent heat-like Lane-Emden equation is solved by using a non-polynomial spline method. An example is solved to assess the accuracy of the method. The numerical results are obtained for different values (n) of equation. The results indicate that non-polynomial spline method is effectively implemented. It is seen that results are compatible with exact solutions and consistent with other existing numerical methods.

show abstract

“…Furthermore, the homotopy analysis method provides us with a family of solution series and a simple way to adjust and control the convergence region and rate of approximation series [48]. Serving as a powerful tool to deal with nonlinear equations, the homotopy analysis method has applied to many nonlinear problems in science and engineering [51,52]. Abbasbandy [53] used the homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation.…”

Section: Introductionmentioning

confidence: 99%

Heat Transfer and Flows of Thermal Convection in a Fluid-Saturated Rotating Porous Medium

Kang

Xia

Liu

2015

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Thermal convection at the steady state for high Rayleigh number in a rotating porous half space is investigated. Taking into account the effect of rotation, Darcy equation is extended to incorporate the Coriolis force term in a rotating reference frame. The velocity and temperature fields of thermal convection are obtained by using the homotopy analysis method. The influences of Taylor number and Rayleigh number on the Nusselt number, velocity profile, and temperature distribution are discussed in detail. It is found that the Nusselt number decreases rapidly with the increase of Taylor number but tends to have an asymptotic value. Besides, the rotation can give rise to downward flow in contrast with the upward thermal convection.

show abstract

Solutions of time-dependent Emden–Fowler type equations by homotopy analysis method

Cited by 97 publications

References 29 publications

Approximate Solution of an Unknown Coefficients in Parabolic Equation

Approximate Solution of an Unknown Coefficients in Parabolic Equation

Non-Polynomial Spline Method for a Time-Dependent Heat-Like Lane- Emden Equation

Heat Transfer and Flows of Thermal Convection in a Fluid-Saturated Rotating Porous Medium

Contact Info

Product

Resources

About