Related papers: Compact difference schemes for the modified anomal…
In mathematical physics, the space-fractional diffusion equations are of particular interest in the studies of physical phenomena modelled by L\'{e}vy processes, which are sometimes called super-diffusion equations. In this article, we…
A modification of the Drude dispersive model based on fractional time derivative is presented. The dielectric susceptibility is calculated analytically and simulated numerically, showing a good agreement between theoretical description and…
We provide and analyze the high order algorithms for the model describing the functional distributions of particles performing anomalous motion with power-law jump length and tempered power-law waiting time. The model is derived in [Wu,…
In 1986, Dixon and McKee developed a discrete fractional Gr\"{o}nwall inequality [Z. Angew. Math. Mech., 66 (1986), pp. 535--544], which can be seen as a generalization of the classical discrete Gr\"{o}nwall inequality. However, this…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…
The present paper deals with the numerical solution of time-fractional advection-diffusion equations involving the Caputo derivative with source term by means of an unconditionally stable implicit finite difference method on quasi-uniform…
In the present work, we propose a new parameterization for the concentration flux using fractional derivatives. The fractional order differential equation in the longitudinal and vertical directions is used to obtain the concentration…
The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The…
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…
The paper is concerned with overlapping domain decomposition and exponential time differencing for the diffusion equation discretized in space by cell-centered finite differences. Two localized exponential time differencing methods are…
We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two…
The Feynman-Kac equations are a type of partial differential equations describing the distribution of functionals of diffusive motion. The probability density function (PDF) of Brownian functionals satisfies the Feynman-Kac formula, being a…
We investigate diffusion equations with time-fractional derivatives of space-dependent variable order. We examine the well-posedness issue and prove that the space-dependent variable order coefficient is uniquely determined among other…
In this paper, a mixed high order finite difference scheme-Pad\'{e} approximation method is applied to obtain numerical solution of the Riesz fractional advection-dispersion equation. This method is based on the high order finite difference…
We present strongly stable semi-discrete finite difference approximations to the quarter space problem (x>0, t>0) for the first order in time, second order in space wave equation with a shift term. We consider space-like (pure outflow) and…
A new method is formulated and analyzed for the approximate solution of a two-dimensional time-fractional diffusion-wave equation. In this method, orthogonal spline collocation is used for the spatial discretization and, for the…
In this paper, we consider finite difference approximations of the second order wave equation. We use finite difference operators satisfying the summation-by-parts property to discretize the equation in space. Boundary conditions and grid…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…
In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…
A generalization of the Gr\"{u}nwald difference approximation for fractional derivatives in terms of a real sequence and its generating function is presented. Properties of the generating function are derived for consistency and order of…