The transport equation (ADE) is one of the pivotal equations in atmospheric sciences and surface/subsurface water quality models. Since analytical methods are at the heart of the verification process in geophysical and environmental fluid mechanics, several analytical solutions have been already derived for this equation. Those previous exact solutions mostly refer to the local mass conservatio...

The turbo decoder was not originally introduced as a solution to an optimization problem. This has made explaining just why the turbo decoder performs as well as it does very difficult. Many authors have attempted to explain both the performance and convergence of the decoder, with varied success. In this document we show that the turbo decoder admits an exact interpretation as an iterative met...

The analysis of acoustic waves generated by a transient normal point load applied on a fluid–solid interface is presented. The closed-form exact solution of the wave motion is obtained by using integral transform techniques. The obtained analytical solution provides necessary theoretical background for optimization of fluid-coupled ultrasonic and acoustic wave detection in experiments. Numerica...

A modified variational approach called Global Error Minimization (GEM) method is developed for obtaining an approximate closed-form analytical solution for nonlinear oscillator differential equations. The proposed method converts the nonlinear differential equation to an equivalentminimization problem. A trial solution is selectedwith unknown parameters. Next, the GEM method is used to solve th...

In this paper we investigate scale-dependent radial two-phase flow of liquid and gas in unsaturated porous media. First we present an equation of two-phase flow of liquid and gas in porous media in radial coordinates (ETPR) based on McWhorter’s equation in Cartesian coordinates. Then we present three analytical solutions for the ETPR: [1] an exact solution of ETPR in three dimensions for radial...

analyzing the nonlinear vibration of beams is one of the important issues in structural engineering. according to this, an impressive analytical method which is called modified iteration perturbation method (mipm) is used to obtain the behavior and frequency of a cantilever beam with geometric nonlinear. this new method is combined by the mickens and iteration methods. moreover, this method don...

The variational iteration method (VIM) proposed by Ji-Haun He is a new analytical method tosolve linear and nonlinear equation. In this paper, the Variational Iteration Method (VIM) has been applied for solving Davey-Stewartson equations which arise as higher dimensional generalizations of the Nonlinear Shrodinger (NLS) equation, as well as from physical considerations [1]. Comparison the absol...

The problem of the boundary layer flow of an incompressible viscous fluid over a non-linear stretching sheet is considered. A spectral collocation method is performed in order to find an analytical solution of the governing nonlinear differential equations. The obtained results are finally compared through the illustrative graphs and tables with the exact solution and some well-known results ob...

Current-sheet formation near a hyperbolic magnetic neutral line in Hall magnetohydrodynamics (MHD) is investigated. An exact analytical solution is given. This solution shows a hastening of the current-sheet formation process at intermediate times by the Hall effect but subsequently a quenching by the Hall effect of the finite-time singularity exhibited in ideal MHD and hence a prevention of th...

The propagation characteristics of a beam generated by driving an aperture with an ultrashort, hence ultrawide-bandwidth, space-time Gaussian pulse are considered. It is shown analytically with an approximate form of the solution that the beam intensity and the beam energy have different diffraction lengths and rates of beam spread in the far field. These beam properties are also discussed for ...