The fractal Toda oscillator with an exponentially nonlinear term is extremely difficult to solve; Elias-Zuniga et al. (2020) suggested the equivalent power-form method. In this paper, first, variational theory used show basic property of oscillator, and a new form obtained free exponential term, which similar Jerk oscillator. homotopy perturbation method solve analytical solution examined using...

This article proposes non-linearities distribution Laplace transform-homotopy perturbation method (NDLT-HPM) to find approximate solutions for linear and nonlinear differential equations with finite boundary conditions. We will see that the method is particularly relevant in case of equations with nonhomogeneous non-polynomial terms. Comparing figures between approximate and exact solutions we ...

I discuss a recent application of homotopy perturbation method to a heat transfer problem. I show that the authors make infinity equal five and analyze the consequences of that magic. There has recently been great interest in the application of several approximate procedures, like the homotopy perturbation method (HPM), the Adomian decomposition method (ADM), and the variation iteration method ...

and Applied Analysis 3 Accordingly, we can construct a homotopy equation in the form ü ω2u p ( u3 −ω2u ) 0. 2.6 When p 0, we have ü ω2u 0, u 0 A, u′ 0 0, 2.7 which describes the basic solution property of the original nonlinear equation, 2.3 . When p 1, 2.6 becomes the original one. So the solution procedure is to deform from the initial solution, 2.4 , to the real one. Due to one unknown param...

Many problems in physics like reconstruction of the radially distributed emissivity from the line-of-sight projected intensity, the 3-D image reconstruction from cone beam projections in computerized tomography, etc. lead naturally, in the case of radial symmetry, to the study of Abel’s type integral equation. Obtaining the physically relevant quantity from the measured one requires, therefore ...

In this paper, a new iterative method for solving the system of nonlinear equations is suggested based on Newton-Raphson method and homotopy analysis method. Comparison of the result obtained by present method with Newton-Raphson method and homotopy perturbation method reveals that the accuracy and fast convergence of the proposed method.

A new perturbation method called the homotopy perturbation method (HPM) [1 – 4] was proposed by Ji-Huan He in 1999, which is a coupling of the traditional perturbation method and homotopy in topology. The traditional perturbation methods are based on assuming a small parameter, and the approximate solutions obtained by those methods, in most cases, are valid only for small values of the small p...

We suggest and analyze a technique by combining the variational iteration method and the homotopy perturbation method. This method is called the variational homotopy perturbation method VHPM . We use this method for solving higher dimensional initial boundary value problemswith variable coefficients. The developed algorithm is quite efficient and is practically well suited for use in these prob...