Related papers: Monotone finite difference schemes for anisotropic…
As is well known that the distribution of the scattered radiation generated by an anisotropic scatterer usually lacks rotational symmetry about the direction of incidence due to the spatial anisotropy of the scatterer itself. Here we show…
We analyze a simple model of deterministic diffusion. The model consists of a one-dimensional periodic array of scatterers in which point particles move from cell to cell as defined by a piecewise linear map. The microscopic chaotic…
In this paper, we consider the solvability of a class of nonlinear fourth order integro-differential equations with Navier boundary condition. We first deal with a corresponding linear problem and establish a maximum principle. Using the…
The work deals with establishing the solvability of a system of integro-differential equations in the situation of the double scale anomalous diffusion. Each equation of such system involves the sum of the two negative Laplace operators…
The maximality principle has been a valuable tool in identifying the free-boundary functions that are associated with the solutions to several optimal stopping problems involving one-dimensional time-homogeneous diffusions and their running…
In this paper we present numerical methods - finite differences and finite elements - for solution of partial differential equation of fractional order in time for one-dimensional space. This equation describes anomalous diffusion which is…
An implicit finite difference method with non-uniform timesteps for solving the fractional diffusion equation in the Caputo form is proposed. The method allows one to build adaptive methods where the size of the timesteps is adjusted to the…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
The analytical solution of the equation describing diffusion of intrinsic point defects has been obtained for a one-dimensional finite-length domain. This solution is intended for investigating and modeling the changes in defect…
An explicit numerical scheme is proposed for solving the initial-boundary value problem for the radiative transport equation in a rectangular domain with completely absorbing boundary condition. An upwind finite difference approximation is…
The diffusion of finite-size hard-core interacting particles in two- or three-dimensional confined domains is considered in the limit that the confinement dimensions become comparable to the particle's dimensions. The result is a nonlinear…
A nonlinear divergence parabolic equation with dynamic boundary conditions of Wentzell type is studied. The existence and uniqueness of a strong solution is obtained as the limit of a finite difference scheme, in the time dependent case and…
The goal of the present work is to solve a linear dispersive equation with variable coefficient advection on an unbounded domain. In this setting, transparent boundary conditions are vital to allow waves to leave (or even re-enter) the,…
We study the finite-momentum spin dynamics in the one-dimensional XXZ spin chain within the Ising-type regime at high temperatures using density autocorrelations within linear response theory and real-time propagation of nonequilibrium…
We introduce a monotone (degenerate elliptic) discretization of the Monge-Ampere operator, on domains discretized on cartesian grids. The scheme is consistent provided the solution hessian condition number is uniformly bounded. Our approach…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
Mechanical models of tumor growth based on a porous medium approach have been attracting a lot of interest both analytically and numerically. In this paper, we study the stability properties of a finite difference scheme for a model where…
We provide sufficient conditions for the continuity of the free-boundary in a general class of finite-horizon optimal stopping problems arising for instance in finance and economics. The underlying process is a strong solution of one…
This paper is devoted to the numerical resolution of an anisotropic non-linear diffusion problem involving a small parameter \varepsilon, defined as the anisotropy strength reciprocal. In this work, the anisotropy is carried by a variable…
This study presents a finite difference method (FDM) to model the electromagnetic field propagation in eccentric coaxial waveguides filled with lossy uniaxially anisotropic media. The formulation utilizes conformal transformation to map the…