Four-dimensional differential transform method has been introduced and fundamental theorems have been defined for the first time. Moreover, as an application of four-dimensional differential transform, exact solutions of nonlinear system of partial differential equations have been investigated. The results of the present method are compared very well with analytical solution of the system. Diff...

Nonequilibrium systems are often characterized by the transport of some quantity at a macroscopic scale, such as, for instance, a current of particles through a wire. The asymmetric simple exclusion process (ASEP) is a paradigm for nonequilibrium transport that is amenable to exact analytical solution. In the present work, we determine the full statistics of the current in the finite size open ...

exact solution for steady two-dimensional flow of an incompressible magma is obtained. themagmatic flow is studied by considering the magma as a second grade fluid. the governing partialdifferential equations are transformed to ordinary differential equations by symmetry transformations. resultsare discussed through graphs to understand the rheology of the flowing magma

In this paper, the homotopyperturbation method (HPM) is employed to obtain approximate analytical solution to the linear and nonlinear systems of partial differential equations (PDEs). HPM yields solutions in convergent series forms with easily computable terms. Generally, the closed form of the exact solution or its expansion is obtained without any noise terms. Test examples demonstrate the e...

In this paper, we consider Adomian Decomposition Method (ADM),and Variational Iteration Method (VIM), Homotopy Analysis Method (HAM), Homotopy Analysis Transform Method (HATM) to solve the FractionalOrder Logistic Equation (FOLE). Comparisons between the approximate analytical solution and exact solution of FOLE are shown. 2010 Mathematics Subject Classication: 34-XX , 34Lxx ,34L30

Phylogenetic diversity (PD) depends on sampling depth, which complicates the comparison of PD between samples of different depth. One approach to dealing with differing sample depth for a given diversity statistic is to rarefy, which means to take a random subset of a given size of the original sample. Exact analytical formulae for the mean and variance of species richness under rarefaction hav...

In this paper, the homotopy perturbation method and a modified homotopy perturbation method are used for analytical treatment of the wave equation and some nonlinear diffusion equations, respectively. Some examples are given to illustrate that a suitable choice of an initial solution can lead to the exact solution, this revealing the reliability and effectiveness of the method. © 2009 Elsevier ...

Many range aggregate queries can be eÆciently derived from a class of fundamental queries: the polynomial range-sums. After demonstrating how any range-sum can be evaluated exactly in the wavelet domain, we introduce a novel pre-aggregation method called ProPolyne to evaluate arbitrary polynomial range-sums progressively. At each step of the computation, ProPolyne makes the best possible wavele...

Because of fluctuation in leg tension, pitch motion is very effective fatigue and life safety of leg elements in tension leg structures (TLSs). In this paper an exact solution for pitch vibration of a TLS interacting with ocean wave is presented. The legs of TLP are considered as elastic springs. The flow is assumed to be irrotational and single-valued velocity potentials are defined. The effec...