in this paper, we present a new two-step trigonometrically fitted symmetric obrechkoff method. the method is based on the symmetric two-step obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve ivps with periodic solutions such as orbital problems. we compare the new method to some recently constructed optimized methods from the literature. the numeri...

In this paper, we investigate the quintessence models with an oscillating equation of state (EoS) and their potentials. From the constructed potentials, which have the EoS of ωφ = ω0+ω1 sin z, we find they are all the oscillating functions of the field φ, and the oscillating amplitudes are decreasing (or increasing) with φ. From the evolutive equation of the field φ, we find this is caused by t...

Acknowledgements: I would like to thank E. Sonnendrücker for the stimulating discussions we had together and from which the problem treated in this paper emerged. Abstract: we show that the solution to an oscillatory-singularly perturbed ordinary differential equation may be asymptotically expanded into a sum of oscillating terms. Each of those terms writes as an oscillating operator acting on ...

This paper describes a preliminary investigation into the use of normal form theory for modelling large non-linear dynamical systems. Limit cycle oscillations are determined for simple two-degree-of-freedom double pendulum systems. The double pendulum system is reduced into its centre manifold before computing normal forms. Normal forms are obtained using a period averaging method which is appl...

As a necessary component, regenerator plays an important role in the refrigeration performance of the pulse tube refrigerator. The objective of this research is to investigate the flow characteristics in a porous regenerator of the pulse tube refrigerators, subjected to oscillating flow. The hydrodynamic and thermal behavior of the regenerator is investigated by considering porous media approac...

If we could realize an autonomous polymer system driven under biological conditions by a tailor-made molecular design, human beings could create unprecedented biomimetic functions and materials such as heartbeats, autonomous peristaltic pumps, etc. In order to achieve this objective, we have investigated the molecular design of such a polymer system. As a result, we were the first to demonstrat...

in this paper, we propose the chebyshev wavelet approximation for the numerical solution of a class of integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. we show that the chebyshev approximation transform an integral equation to an explicit system of linear algebraic equations. illustrative examples are included t...

in this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. the homotopy analysis method (ham) is used for solving this equation. several examples are given to reconfirm the efficiency of these algorithms. the results of applying this procedure...

In this paper, we give an analytical approximate solution for an integro- differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields is considered. The homotopy analysis method (HAM) is used for solving this equation. Several examples are given to reconfirm the efficiency of these algorithms. The results of applying this procedure...

We study the homogenization problem for a random parabolic operator with coefficients rapidly oscillating in both the space and time variables and with a large highly oscillating nonlinear potential, in a general stationary and mixing random media, which is periodic in space. It is shown that a solution of the corresponding Cauchy problem converges in law to a solution of a limit stochastic PDE...