A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick’s law. In this paper we combine the forward time centered space (FTCS) method, well k...

An implicit, time-dependent variable grid finite difference method based on the addition of an artificial diffusivity is introduced and analyzed for approximating the solution of a scalar conservation law in a single space variable. No relation between the grids at successive time steps is required for convergence. Two adaptive grid selection procedures are shown to be covered by the analysis. ...

This work is the numerical analysis and computational companion of the paper by Kamgang and Sallet (Math. Biosc. 213 (2008), pp. 1–12) where threshold conditions for epidemiological models and the global stability of the disease-free equilibrium (DFE) are studied. We establish a discrete counterpart of the main continuous result that guarantees the global asymptotic stability (GAS) of the DFE f...

The hepatitis B infection is a global epidemic disease which huge risk to the public health. In this paper, transmission dynamics of deterministic model are presented and studied. basic reproduction number attained by applying it, local as well stability disease-free endemic equilibria continuous discussed. To better understand disease, discrete nonstandard finite difference (NSFD) scheme produ...

Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...

in this paper, a parameter uniform numerical method based on shishkin mesh is suggested to solve a system of second order singularly perturbed differential equations with a turning point exhibiting boundary layers. it is assumed that both equations have a turning point at the same point. an appropriate piecewise uniform mesh is considered and a classical finite difference scheme is applied on t...

an analysis is carried out to investigate the effects of variable chemical reaction, thermophoresis, temperaturedependent viscosity and thermal radiation on an unsteady mhd free convective heat and mass transfer flow of a viscous, incompressible, electrically conducting fluid past an impulsively started infinite inclined porous plate by taking into account the viscous dissipation effects. the g...

In this paper we analyze an implicit finite difference scheme for the mixed initial-value Dirichlet problem for a system of two conservation laws with artificial viscosity. The system we consider is a model for'isentropic flow in one space dimension. First, we show that, under certain conditions on the mesh, the scheme is stable in the sense that it possesses an invariant set (defined by the so...

In this paper, we present an MATLAB version of a finite difference scheme for the numerical solution of the American option valuation problem. Our main contribute is the definition of a posteriori error estimator for the American options pricing which is based on Richardson’s extrapolation theory. This error estimator allows us to find a suitable grid where the computed solution, both the optio...

in this work, we apply the radial basis functions for solving the time fractional diffusion-wave equation defined by caputo sense for                         . the problem is discretized in the time direction based on finite difference scheme and is continuously approximated by using the radial basis functions in the space direction which achieves the semi-discrete solution. numerical results s...