on the basis of a reproducing kernel space, an iterative algorithm for solving the one-dimensional linear and nonlinear schrödinger equations is presented. the analytical solution is shown in a series form in the reproducing kernel space and the approximate solution is constructed by truncating the series. the convergence of the approximate solution to the analytical solution is also proved. th...

We intend to present an approximate analytic solution of the two-body problem with slowly decreasing mass which is obtained through the integration of the Hamilton equations using A. Deprit’s method of perturbations. The solution, obtained through the law of mass variation ṁ = −αmn is put into practice in a specific case and compared with F. Mestschersky’s exact equation (n = 2) and with that w...

Approximations are commonly employed to find approximate solutions to the Einstein equations. These solutions, however, are usually only valid in some specific spacetime region. A global solution can be constructed by gluing approximate solutions together, but this procedure is difficult because discontinuities can arise, leading to large violations of the Einstein equations. In this paper, we ...

The solution y(x) of an IVP for a linear ODE with analytic coefficient functions is represented as a power series. A high–order Taylor polynomial is used for an approximate numerical solution. The Taylor remainder series is rigorously estimated by some geometric series. The method has been implemented and tested on a computer. Guaranteed enclosures are achieved by taking into account all roundo...

We present a KAM theory for some dissipative systems (geometrically, these are conformally symplectic systems, i.e. systems that transform a symplectic form into a multiple of itself). For systems with n degrees of freedom depending on n parameters we show that it is possible to find solutions with n-dimensional (Diophantine) frequencies by adjusting the parameters. We do not assume that the sy...

Analytic and numerical models are used to study bone-conducted sound and how it relates to the vibrational modes of the human skull. The analytic model is based on the solution to the acoustic and elastic wave equations and the constraining boundary conditions for a fluid-filled elastic sphere. Both models predict that most of the acoustic energy of bone-conducted sound exists in the form of su...

Fractional differential equations started to have important applications in various fields of science and engineering involving dynamics of complex phenomena. Finding new methods to solve the fractional differential equations is an open issue in the area of fractional calculus. In this paper the homotopy perturbation method is used to find an analytic approximate solution for the coupled Lotka-...

In this paper, we expand on an idea for using Krylov subspace information for the matrix A and the vector b. This subspace can be used for the approximate solution of a linear system f(A)x = b, where f is some analytic function. We will make suggestions on how to use this for the case where f is the matrix sign function.

The cumulative beam breakup problem excited by the resistive-wall wake is formulated. An approximate analytic method of finding the asymptotic behavior for the transverse bunch displacement is developed and solved. Comparison between the asymptotic analytical expression and the direct numerical solution is presented. Good agreement is found. The criterion of using the asymptotic analytical expr...