In the present study, analytical solutions are developed for three-dimensional advection-dispersion equation (ADE) in semi-infinite adsorbing saturated homogeneous porous medium with time dependent dispersion coefficient. It means porosity of the medium is filled with single fluid(water). Dispersion coefficient is considered proportional to seepage velocity while adsorption coefficient inversel...

In the present study, analytical solutions are developed for three-dimensional advection-dispersion equation (ADE) in semi-infinite adsorbing saturated homogeneous porous medium with time dependent dispersion coefficient. It means porosity of the medium is filled with single fluid(water). Dispersion coefficient is considered proportional to seepage velocity while adsorption coefficient inversel...

We propose a reachability verification technique that combines the Petri net state equation (a linear algebraic overapproximation of the set of reachable states) with the concept of counterexample guided abstraction refinement. In essence, we replace the search through the set of reachable states by a search through the space of solutions of the state equation. We demonstrate the excellent perf...

We extend He’s variational iteration method VIM to find the approximate solutions for nonlinear differential-difference equation. Simple but typical examples are applied to illustrate the validity and great potential of the generalized variational iteration method in solving nonlinear differentialdifference equation. The results reveal that the method is very effective and simple. We find the e...

phenomena, overstating the need for simulational tools that can handle multiple space and time scales is hard. The capability of addressing problems across several length and time scales is a hallmark of modern computational science, the goal of which is to tackle issues that straddle various traditional disciplines of science and engineering. Some interesting examples of such phenomena that ha...

Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations. Based on the good performance, Chen and Wu presented a kind of multiquadric (MQ) quasi-interpolation, which is generalized from the LD operator, and used it to solve hyperbolic conservation laws and Burgers’...

We consider the inviscid Burgers' equation enlarged with a control function and its adjoint equation. For several discretization schemes of the inviscid Burgers' equation the \adjoint" nite diier-ence methods are derived. Applying these discretization methods and the checkpointing routine treeverse, approximations of the solution of both diierential equations are calculated and compared. 1 The ...

assume that $mathbb{d}$ is the open unit disk. applying ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{g}(alpha)$ and $mathcal{f}(mu)$ as follows begin{equation*}  mathcal{g}(alpha):=left{fin mathcal{a}:mathfrak{re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right)

Medicinal plants provide indigenous and peasant communities worldwide with means to meet their healthcare needs. Homegardens often act as medicine cabinets, providing easily accessible medicinal plants for household needs. Social structure and social exchanges have been proposed as factors influencing the species diversity that people maintain in their homegardens. Here, we assess the associati...