We consider one-dimensional systems in the presence of a quasi-periodic perturbation, in the analytical setting, and study the problem of existence of quasi-periodic solutions which are resonant with the frequency vector of the perturbation. We assume that the unperturbed system is locally integrable and anisochronous, and that the frequency vector of the perturbation satisfies the Bryuno condi...

in this paper, we implemented the modified iteration perturbation method (mipm) for approximating the periodic behavior of a tapered beam. this problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. the solution is quickly convergent and does not need to complicated calculations. comparing the results of the mipm with the exact solution shows that t...

An accurate theory describing adiabatic following of the dark, nonabsorbing state in the three-level system is developed. An analytical solution for the wave function of the particle experiencing Raman excitation is found as an expansion in terms of the time varying nonadiabatic perturbation parameter. The solution can be presented as a sum of adiabatic and nonadiabatic parts. Both are estimate...

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...

It is well-known that the matrix equations play a significant role in several applications in science and engineering. There are various approaches either direct methods or iterative methods to evaluate the solution of these equations. In this research article, the homotopy perturbation method (HPM) will employ to deduce the approximated solution of the linear matrix equation in the form AXB=C....

In this paper, we adapt the operational Tau Method for personal computers and apply it to a system of two nonlinear second order ordinary differential equations which are related to general relativity. The interesting behaviour this problem exhibits in its numerical treatment is discussed. In this problem, we try to use the Tau perturbation term to locate the correct solution of this nonlin...