Two binary stars gravitational waves - homotopy perturbation method

Homotopy perturbation is one of the newest methods for numerical analysis of deferential equations. We have used for solving wave equation around a black hole. Our conclusions have this method far reaching consequences for comparison of theoritical physics and experimental physics.Comment: The manuscript considers the important problem of solve equation wave around a black hole. We have solved that by using Homotopy perturbation methods. Homotopy perturbation is one of the newest methods for numerical analysis of deferential equations. Our conclusions have far reaching consequences for comparison of theoritical physics and experimental physic

Comparison of homotopy analysis method and homotopy-perturbation method for purely nonlinear fin-type problems

In this paper, the homotopy analysis method (HAM) is compared with the homotopy-perturbation method (HPM) and the Adomian decomposition method (ADM) to determine the temperature distribution of a straight rectangular fin with power-law temperature dependent surface heat flux. Comparisons of the results obtained by the HAM with that obtained by the ADM and HPM suggest that both the HPM and ADM are special case of the HAM

THE ENHANCED HOMOTOPY PERTURBATION METHOD FOR AXIAL VIBRATION OF STRINGS

A governing equation is established for string axial vibrations with temporal and spatial damping forces by the Hamilton principle. It is an extension of the well-known Klein-Gordon equation. The classical homotopy perturbation method (HPM) fails to analyze this equation, and a modification with an exponential decay parameter is suggested. The analysis shows that the amplitude behaves as an exponential decay by the damping parameter. Furthermore, the frequency equation is established and the stability condition is performed. The modified homotopy perturbation method yields a more effective result for the nonlinear oscillators and helps to overcome the shortcoming of the classical approach. The comparison between the analytical solution and the numerical solution shows an excellent agreement

On Modified Algorithm for Fourth-Grade Fluid

This paper shows the analysis of the thin film flow of fourth-grade fluid on the outer side of a vertical cylinder. Solution of the governing nonlinear equation is obtained by Rational Homotopy Perturbation Method (RHPM); comparison with exact solution reflects the reliability of the method. Analysis shows that this method is reliable for even high nonlinearity. Graphs and tables strengthen the idea

New analytical approximate solutions of Fifth-order KdV equation

In this paper, we have exposed a process of how to implement a new splitting Adomian decomposition homotopy perturbation method to solve fifth-order KdV equations. The new methodology is applied on two kinds of fifth-order KdV equations with initial data: The first is Sawada-Kotera equation and the second its Lax equation. The numerical results we  obtained  from solutions of two kinds of fifth-order KdV equations, have good convergent  and high  accuracy  comparison with other methods in literature. The graphs and tables of the new analytical approximate solutions show the validity, usefulness, and necessity of the process. Keywords: Splitting scheme, Adomian decomposition, homotopy perturbation method,  fifth-order KdV equation, convergence analysis. Mathematics Subject Classifications 2010 [MSC]: 76S05, 65N99, 35Q3

Traveltime approximation for strongly anisotropic media using the homotopy analysis method

Traveltime approximation plays an important role in seismic data processing, for example, anisotropic parameter estimation and seismic imaging. By exploiting seismic traveltimes, it is possible to improve the accuracy of anisotropic parameter estimation and the resolution of seismic imaging. Conventionally, the traveltime approximations in anisotropic media are obtained by expanding the anisotropic eikonal equation in terms of the anisotropic parameters and the elliptically anisotropic eikonal equation based on perturbation theory. Such an expansion assumes a small perturbation and weak anisotropy. In a realistic medium, however, the assumption of small perturbation likely breaks down. We present a retrieved zero-order deformation equation that creates a map from the anisotropic eikonal equation to a linearized partial differential equation system based on the homotopy analysis method. By choosing the linear and nonlinear operators in the retrieved zero-order deformation equation, we develop new traveltime approximations that allow us to compute the traveltimes for a medium of arbitrarily strength anisotropy. A comparison of the traveltimes and their errors from the homotopy analysis method and from the perturbation method suggests that the traveltime approximations provide a more reliable result in strongly anisotropic media.publishedVersio