On the Homotopy Analysis Method and Optimal Value of the Convergence Control Parameter: Solution of Euler-Lagrange Equation

Saberi‐Nadjafi, Jafar; Buzhabadi, R.; Nik, Hassan Saberi

doi:10.4236/am.2012.38129

Cited by 3 publications

(1 citation statement)

References 16 publications

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“…In (Madani et al (2011)), the couple Laplace transform-homotopy perturbation method is employed for solving one dimensional non-homogenous partial differential equations with a variable coefficient. The used method is a combination of the Laplace transform and the hmomotopy perturbation method (He (2006), Saberi-Nadjafi et al (2012)). In the present section we determine a new form of solution for the studied problem using the Laplace transform coupled with the homomtopy perturbation method.…”

Section: Homotopy Perturbation Methodsmentioning

confidence: 99%

The Influence of Ekman Number on Flows Over an Oscillating Isothermal Vertical Plate in a Rotating Frame

Imran¹,

Vieru²,

Mirza³

2015

JAFM

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Unsteady flows of a Newtonian fluid past an oscillating infinite isothermal vertical plate in a rotating frame are studied. Two closed forms of the velocity field are determined by means of Laplace transform method and by the technique of coupling of the homotopy perturbation method with the Laplace transform method. The equivalence of the obtained expressions for the velocity is provided. The friction coefficients are determined and, the influence of Ekman number on the velocity field is analyzed by graphical illustrations. It is obtained that, the faster frame rotations reduce the thickness of moving fluid layer.

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Section: Homotopy Perturbation Methodsmentioning

confidence: 99%

The Influence of Ekman Number on Flows Over an Oscillating Isothermal Vertical Plate in a Rotating Frame

Imran¹,

Vieru²,

Mirza³

2015

JAFM

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Approximating photon trajectories in spherically symmetric spacetimes

Sultana

2024

Gen Relativ Gravit

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In this paper we use the Homotopy analysis method to obtain an analytic approximation for the entire photon trajectory in the Schwarzschild spacetime. This is usually expressed exactly in terms of an elliptic integral. We compare our approximation with other formulae found in the literature, which were specifically obtained for the Schwarzschild solution. Unlike some of these formulae, our approximation can be applied and maintains a good accuracy for emission point close to the event horizon and also for emission angles close to and greater than $$\pi /2$$ π / 2 . We show that our method can easily be applied to other spherically symmetric solutions such as the Reissner-Nordström solution. Such an approximation would be useful when accurate determination of the light trajectories around compact objects is required without the need to revert to time consuming numerical integration of elliptic integrals.

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The Study of Heat and Mass Transfer in a Visco Elastic Fluid Due to a Continuous Stretching Surface Using Homotopy Analysis Method

Seshadri

Munjam²

2014

jaac

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On the Homotopy Analysis Method and Optimal Value of the Convergence Control Parameter: Solution of Euler-Lagrange Equation

Cited by 3 publications

References 16 publications

The Influence of Ekman Number on Flows Over an Oscillating Isothermal Vertical Plate in a Rotating Frame

The Influence of Ekman Number on Flows Over an Oscillating Isothermal Vertical Plate in a Rotating Frame

Approximating photon trajectories in spherically symmetric spacetimes

The Study of Heat and Mass Transfer in a Visco Elastic Fluid Due to a Continuous Stretching Surface Using Homotopy Analysis Method

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