In this paper, the homotopy Pade technique is presented as an alternative method to derive the analytical solution for nonlinear dynamical system. Illustrative example is used to show the validity and accuracy of the method in solving the nonlinear system. Comparisons are conducted between the analytical approximation and numerical solution. The results obtained here demonstrate that the homoto...

Analytical solutions are attractive for parametric studies and consideration of the problems physics. In addition, analytical solutions can be employed as a reference framewo...

In this paper, Homotopy Analysis Method is used to analyze free non-linear vibrations of a beam simply supported by pinned ends under axial force. Mid-plane stretching is also considered for dynamic equation extracted for the beam. Galerkin decomposition technique is used to transform a partial dimensionless nonlinear differential equation of dynamic motion into an ordinary nonlinear differenti...

The nonlinear oscillator problem has extensive applications. In this paper, we examined the modified homotopy perturbation method to obtain the solution of the problem and to reduce the computational efforts. For the accuracy purpose the Laplace transform and Pade approximation have also been used. We construct the deformation equations by two components of the homotopy series, then by means of...

the work  addressed in this paper is a comparative study between convergence of the  acceleration techniques, diagonal pad'{e} approximants and shanks transforms, on homotopy analysis method  and adomian decomposition method for solving  differential equations of integer and fractional orders.

An efficient and accurate analytical solution is provided using the homotopy-Pade technique for the nonlinear vibration of parametrically excited cantilever beams. The model is based on the Euler-Bernoulli assumption and includes third order nonlinear terms arisen from the inertial and curvature nonlinearities. The Galerkin’s method is used to convert the equation of motion to a nonlinear ordin...

in this paper, the magnetohydrodynamic (mhd) boundary layer flow over a nonlinear porous stretching sheet is investigated by employing the homotopy perturbation transform method (hptm) and the pade´ approximation. the numerical solution of the governing non-linear problem is developed. comparison of the present solution is made with the existing solution and excellent agreement is noted. graphi...

In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtainedusing theHomotopyAnalysisMethod (HAM) andHomotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results andnumerical solutions shows that only the first order approximation of the Homotopy ...

in this paper, a reliable approach is introduced to approximate periodic solutions of a system of coupled integrable dispersionless. the system is firstly, transformed into an ordinary differential equation by wave transformation. the solution of ode is obtained by the homotopy perturbation method. to show the periodic behavior of the solution, a modification based on the laplace transforms and...

This paper proposed an efficient modification of homotopy perturbation transform method (HPTM), namely modified homotopy perturbation transform method (MHPTM) for the solution of third order boundary layer equation on semi-infinite domain. The technique was based on the application of Laplace transform to boundary layers in fluid mechanics. The nonlinear terms can be easily handled by the use o...