We study a probabilistic numerical scheme to solve the incompressible Navier-Stokes equations, in which we approximate a generalized nonlinear Feyman-Kac formula. The velocity field is interpreted as the mean value of a stochastic process ruled by Forward-Backward Stochastic Differential Equations (FBSDEs). Using a representation by Del-baen, Qiu a...
Published in Journal of Surface Investigation: X-ray, Synchrotron and Neutron Techniques
AbstrtactThe propagation of wave packets of quantum particles through porous structures in thin semi-transparent films is studied. Numerical solution of the nonstationary Schrödinger equation is used in two-dimensional (for slits) and three-dimensional (round holes) cases. The transmission coefficient of quantum particles is compared with that of c...
Published in Chemosphere
Two new adsorbents, namely avocado-based hydrochar and LDH/bone-based biochar, were developed, characterized, and applied for adsorbing 2-nitrophenol. The pore volume and surface diffusion model (PVSDM) was numerically solved for different geometries and applied to interpret the adsorption decay curves. Both adsorbents presented interesting textura...
Published in Journal of Applied and Industrial Mathematics
Abstract Some algorithm is presented for solving the convolution type Volterra integral equation of the first kind by the quadrature-sum method. We assume that the integral equation of the first kind cannot be reduced to an integral equation of the second kind but we do not assume that either the kernel or some of its derivatives at zero are unequa...
The ruin probability is used to determine the overall operating risk of an insurance company. Modeling risks through the characteristics of the historical data of an insurance business, such as premium income, dividends and reinvestments, can usually produce an integral differential equation that is satisfied by the ruin probability. However, the d...
Published in Computational Mathematics and Mathematical Physics
AbstractA three-dimensional scalar stationary scattering problem is considered. It is formulated in the form of a weakly singular Fredholm boundary integral equation of the first kind with a single unknown function. The equation is approximated by a system of linear algebraic equations, which is then solved numerically by an iterative method. The m...
In the present study, our aim is to present a novel model for the flow of hybrid nanofluids in oblique channels. Copper and aluminum oxide have been used to obtain a novel hybrid nanofluid. The equations that govern the flow of hybrid nanofluids have been transformed to a set of nonlinear equations with the implementation of self-similar variables....
Published in Lobachevskii Journal of Mathematics
AbstractWe present a problem described by Mean Field Games (MFG) and Optimal Control theory on finite time horizon. This problem consists of a system of PDEs: a Kolmogorov–Fokker–Planck equation, evolving forward in time and a Hamilton–Jacobi–Bellman equation, evolving backwards in time. The numerical difficulties are based on a turnpike effect con...
Published in Computational Mathematics and Mathematical Physics
AbstractA control problem for an integro-differential equation is approximated by a problem with parameter for a loaded differential equation. A mutual relationship between the qualitative properties of the original and approximate problems is obtained, and estimates for the differences between their solutions are given. A numerical-approximate met...
In this paper, we study the interactions between microglia and neural stem cells and the impact of these interactions on the brain cells during a stroke. Microglia cells, neural stem cells, the damage on brain cells from the stroke and the impacts these interactions have on living brain cells are considered in the design of mathematical models. The...
