As an effective method for solving linear and nonlinear equations, the homotopy perturbation is usually applied to relevant problems. We analyze 74 studies on application of present a comprehensive review them with conclusion obtained: (1) Homotopy generally problems ordinary differential equations; (2) combined technology transform when it used solve more complicated (3) By comparing other sim...

We define a new method for global optimization, the Homotopy Optimization Method (HOM). This method differs from previous homotopy and continuation methods in that its aim is to find a minimizer for each of a set of values of the homotopy parameter, rather than to follow a path of minimizers. We define a second method, called HOPE, by allowing HOM to follow an ensemble of points obtained by per...

A natural number m is called the homotopy minimal period of a map f : X → X if it is a minimal period for every map g homotopic to f. The set HPer (f) of all minimal homotopy periods is an invariant of the dynamics of f which is the same for a small perturbation of f. In this paper we give a complete description of the sets of homotopy minimal periods of selfmaps of nonabelian three dimensional...

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...

In this paper, quadratic nonlinear oscillators under stochastic excitation are considered. The Wiener-Hermite expansion with perturbation (WHEP) method and the homotopy perturbation method (HPM) are used and compared. Different approximation orders are considered and statistical moments are computed in the two methods. The two methods show efficiency in estimating the stochastic response of the...

In this paper, we prove the convergence of homotopy analysis method (HAM). We also apply the homotopy analysis method to obtain approximate analytical solutions of systems of the second kind Volterra integral equations. The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of series solutions. It is shown that the solutions obtain...

The homotopy analysis method HAM is employed to obtain symbolic approximate solutions for nonlinear coupled equations with parameters derivative. These nonlinear coupled equations with parameters derivative contain many important mathematical physics equations and reaction diffusion equations. By choosing different values of the parameters in general formal numerical solutions, as a result, a v...