Related papers: Penalty Method for Reflected Diffusions on the Hal…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
We are interested in the numerical solution of nonsymmetric linear systems arising from the discretization of convection-diffusion partial differential equations with separable coefficients and dominant convection. Preconditioners based on…
The differential cross-section for the reflection of light beams off rigid bodies obtained by the rotation of a generic derivable convex function is calculated. The calculation is developed using elementary notions of calculus and is…
A particle subject to a white noise external forcing moves like a Langevin process. Consider now that the particle is reflected at a boundary which restores a portion c of the incoming speed at each bounce. For c strictly smaller than the…
We propose an implicit iterative algorithm for an exact penalty method arising from inequality constrained optimization problems. A rapidly convergent fixed point method is developed for a regularized penalty functional. The applicability…
Two methods of refractometry in reflected light from optical surface of samples are considered and studied experimentally. Methods are grounded on results of Fresnel theory of concerning light reflectivity at near normal incidence and…
The problem of a beam of quantum particles falling through a diffractive screen is studied. The solutions for single and double slits are obtained explicitly when the potential is approximated by a linear function. It is found that the…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
We consider the dividend maximization problem including a ruin penalty in a diffusion environment. The additional penalty term is motivated by a constraint on dividend strategies. Intentionally, we use different discount rates for the…
A one dimensional fractional diffusion model with the Riemann-Liouville fractional derivative is studied. First, a second order discretization for this derivative is presented and then an unconditionally stable weighted average finite…
We derive a diffusion approximation for the kinetic Vlasov-Fokker-Planck equation in bounded spatial domains with specular reflection type boundary conditions. The method of proof involves the construction of a particular class of test…
We consider a dimer formed by two particles with an attractive contact interaction in one dimension, colliding with a hard wall. We compute the scattering phase shifts and the reflection coefficients for various collision energies and…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
We prove existence and uniqueness of the solution of a one-dimensional rough differential equation driven by a step-2 rough path and reflected at zero. In order to deal with the lack of control of the reflection measure the proof uses some…
A time-discretization of the stochastic incompressible Navier--Stokes problem by penalty method is analyzed. Some error estimates are derived, combined, and eventually arrive at a speed of convergence in probability of order 1/4 of the main…
We investigate the fractional diffusion approximation of a kinetic equation set in a bounded interval with diffusive reflection conditions at the boundary. In an appropriate singular limit corresponding to small Knudsen number and long time…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
This is a review of statistical inference methodology for stochastic differential equations driven by fractional Brownian motion, otherwise called fractional diffusions. The first section reviews the theory needed to rigorously define them.…
In order to accelerate the Douglas--Rachford method we recently developed the circumcentered--reflection method, which provides the closest iterate to the solution among all points relying on successive reflections, for the best…
In this article, we consider numerical schemes for polynomial diffusions on the unit ball, which are solutions of stochastic differential equations with a diffusion coefficient of the form $\sqrt{1-|x|^{2}}$. We introduce a semi-implicit…