An approximate analytic model is presented to describe spatial structure of refracted electromagnetic field arising at oblique incidence of a Gaussian beam on a plane boundary of an absorbing homogeneous medium. The analytic solution is obtained by asymptotic approximation of a Fourier field integral under the condition of great beam width in comparison with a wavelength (the geometrical-optics...

In this paper, we study a reducible method which is called linearization(Linear-transform) for some non-linear stochastic differential equations (SDEs) to linear by using the Ito-integrated formula. And then finding their analytic solution, compare obtained solution nonlinear SDEs with approximate numerical (Euler -Maruyama and Milstein) Methods.

The homotopy perturbation method is used to find an approximate analytic solution of the problem involving a space-time fractional diffusion equation with a moving boundary. This mathematical technique is used to solve the problem which performs extremely well in terms of efficiency and simplicity. Numerical solutions of the problem reveal that only a few iterations are needed to obtain accurat...

In this paper we applied a new analytic approximate technique Optimal Homotopy Asymptotic Method (OHAM) for treatment of coupled differential-difference equations (DDEs). To see the efficiency and reliability of the method, we consider Relativistic Toda coupled nonlinear differential-difference equation. It provides us a convenient way to control the convergence of approximate solutions when it...

A cutting plane algorithm for minimizing a convex function subject to constraints deened by a separation oracle is presented. The algorithm is based on approximate analytic centers. The nonlinearity of the objective function is taken into account, yet the feasible region is approximated by a containing polytope. This containing polytope is regularly updated by adding a new cut through a test po...

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...

a new modified adomian decomposition method (adm) is utilized to obtain an analytical solution for buckling of the nanocantilever actuators immersed in liquid electrolytes. the nanoactuators in electrolytes are subject to different nonlinear forces including ionic concentration, van der waals, external voltage and electrochemical forces. the duan–rach modified adomian decomposition method is ut...

This paper begins by giving the results obtained by the Crank-Gupta method and Gupta-Banik method for the oxygen diffusion problem in absorbing tissue, and then we propose a new resolution method for this problem by the Adomian decomposition method. An approximate analytical solution is obtained, which is demonstrated to be quite accurate by comparison with the numerical and approximate solutio...