We formulate the generalized master equation for a class of continuous-time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this master equation, we also derive reaction-diffusion equations for subdiffusive chemical species, using a mean-f...

Penelitian ini merupakan penelitian murni berupa kajian teori tentang solusi persamaan difusi adveksi dengan metode pemisahan variabel. Tujuan dari adalah untuk mengetahui penurunan adveksi, menemukan menggunakan variabel dan melakukan simulasi Solusi Persamaan software Matlab. Difusi Adveksi diperoleh Hukum Fick. menerapkan variabel, menentukan syarat batas, memisahkan mendapatkan umum, khusus...

This article discusses the results of an experimental survey on the performance of a select group of open boundary conditions (OBCs) for threedimensional, primitive equation models. The focus is on passive conditions, where the model response at the open boundaries is dictated by the interior dynamics. The performance of the OBCs is tested in a series of numerical experiments conducted in a rot...

Water pollution by industrial and agricultural waste is an increasingly major public health issue. It is therefore important for water engineers and managers to be able to predict accurately the local behaviour of water-borne pollutants. This paper describes the novel and ecient coupling of dynamically adaptive hierarchical grids with standard solvers of the advection±di€usion equation. Adapti...

We consider the problem of numerically approximating the solution of the coupling of the flow equation in a porous medium, with the advection-diffusion equation in the presence of uncertainty on the permeability of the medium. Random coefficients are classically used in the flow equation to modelize uncertainty. More precisely, we propose the numerical analysis of a method developed to compute ...

Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-water hydrology, are scattered across the literature, and not always well known. In this two-part s...

In this paper, we propose a new conservative hybrid finite element-finite difference method for the Vlasov equation. The proposed methodology uses Strang splitting to decouple the nonlinear high dimensional Vlasov equation into two lower dimensional equations, which describe spatial advection and velocity acceleration/deceleration processes respectively. We then propose to use a semi-Lagrangian...

In this paper, we consider a variable-order fractional advection-diffusion equation with a nonlinear source term on a finite domain. Explicit and implicit Euler approximations for the equation are proposed. Stability and convergence of the methods are discussed. Moveover, we also present a fractional method of lines, a matrix transfer technique, and an extrapolation method for the equation. Som...