in the present study a quasi 2-d numerical model is developed for calculating air concentration distribution in rapid flows. the model solves air continuity equation (convection diffusion equation) in the whole flow domain. this solution is then coupled with calculations of the free surface in which air content in the flow is also considered. to verify the model, its results are compared with a...

For the backward diffusion equation, a stable discrete energy regularization algorithm is proposed. Existence and uniqueness of the numerical solution are given. Moreover, the error between the solution of the given backward diffusion equation and the numerical solution via the regularization method can be estimated. Some numerical experiments illustrate the efficiency of the method, and its ap...

The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameter ε, of first order in the discrete ...

introduction : due to the importance of laser light penetration and propagation in biological tissues, many researchers have proposed several numerical methods such as monte carlo, finite element and green function methods. among them, the monte carlo method is an accurate method which can be applied for different tissues. however, because of its statistical nature, monte carlo simulation requi...

Variable-order fractional diffusion equation model is a recently developed and promising approach to characterize time-dependent or concentration-dependent anomalous diffusion, or diffusion process in inhomogeneous porous media. To further study the properties of variableorder time fractional subdiffusion equation models, the efficient numerical schemes are urgently needed. This paper investiga...

Fractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Fractional nonlinear reaction-diffusion models have found numerous applications in patten formation in biology, chemistry, physics and Engineering. Obtaining analytical solutions of fractional nonlinear reaction-diffusion models is difficult, generally numerica...

Modeling diffusion processes, such as drug deliver, bio-heat transfer, and the concentration change of cytokine for computational biology research, requires intensive computing resources as one must employ sequential numerical algorithms to obtain accurate numerical solutions, especially for real-time in vivo 3D simulation. Thus, it is necessary to develop a new numerical algorithm compatible w...

Cross-diffusion driven instabilities have gained a considerable attention in the field of population dynamics, mainly due to their ability to predict some important features in the study of the spatial distribution of species in ecological systems. This paper is concerned with some mathematical and numerical aspects of a particular reaction–diffusion system with cross-diffusion, modeling the ef...

We develop a maximum penalized quasi-likelihood estimator for estimating in a nonparametric way the diffusion function of a diffusion process, as an alternative to more traditional kernel-based estimators. After developing a numerical scheme for computing the maximizer of the penalized maximum quasi-likelihood function, we study the asymptotic properties of our estimator by way of simulation. U...

The dual-reciprocity boundary element method is applied for the numerical solution of a class of two-dimensional initial-boundary value problems governed by a non-linear system of partial differential equations. The system, known as the reaction-diffusion Brusselator, arises in the modeling of certain chemical reaction-diffusion processes. Numerical results are presented for some specific probl...