We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time limit, is characterized by a universal power law. Contrasting this power law with the asymptotic FPT distribution from another type of anomalous diffusion exe...

We study, both analytically and by numerical modeling the equilibrium probability density function for an non-linear Lévy oscillator with the Lévy index α, 1 ≤ α ≤ 2, and the potential energy x 4. In particular, we show that the equilibrium PDF is bimodal and has power law asymptotics with the exponent −(α + 3). 1 Starting equations Recently, kinetic equations with fractional derivatives have a...

A new modified diffusi on coefficient (MDC) technique for solv ing conve ction diffusion equation is proposed. The Galerkin finite-element discretization process is applied on the modified equation rather than the original one. For a class of one-dimensional convec-tion–diffusion equations, we derive the modi fied diffusion coefficient analytically as a function of the equation coefficients and...

We present a multigrid method for the solution of convection diffusion equations that is based on the combination of recursive substructuring techniques and the discretization on hierarchical bases and generating systems. Robustness of the resulting method, at least for a variety of benchmark problems, is achieved by a partial elimination between certain "coarse grid unknowns". The choice of th...

We study the homogenization problem for a convection-diffusion equation in a periodic porous medium in the presence of chemical reaction on the pores surface. Mathematically this model is described in terms of a solution to a system of convection-diffusion equation in the medium and ordinary differential equation defined on the pores surface. These equations are coupled through the boundary con...

An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary conditions of Robin type. Finite element approximation in space is employed. To construct approximation in time, regularized twolevel schemes are used. The numeri...

Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...