the aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (pde) in the electroanalytical chemistry. the space fractional derivative is described in the riemann-liouville sense. in the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the grunwald- letnikov discretization of the ri...

in chemical engineering, several processes are represented by singular boundary value problems. in general, classical numerical methods fail to produce good approximations for the singular boundary value problems. in this paper, chebyshev finite difference (chfd) method and dtm-pad´e method, which is a combination of differential transform method (dtm) and pad´e approximant, are applied for sol...

The popular reaction–diffusion model for the negative bias temperature instability is discussed from the viewpoint of stochastic chemical kinetics. We present a microscopic formulation of the reaction–diffusion model based on the reaction–diffusion master equation and solve it using the stochastic simulation algorithm. The calculations are compared to the macroscopic version as well as establis...

In this article, we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear Robin-type boundary conditions. We then state and prove the necessary conditions for diffusion-driven instability for the coupled system. Owing to the nature o...

Linearly-implicit, approximate factorization methods are used to reduce the solution of multi-dimensional reaction–diffusion equations to a sequence of two-point boundaryvalue problems in ordinary differential equations which are solved analytically in a piecewise manner. It is shown that, depending on the allocation of the transient, diffusion and reaction terms to the second-order ordinary di...

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...

This paper demonstrates some examples that show the ability of reaction-diffusion mechanism to code the curvature of forms of multi-cellular systems. The simulation model consists of two layers: the first generates reaction-diffusion waves and the second diffuses chemical substances. The results show that topology changes feedback information to the reaction-diffusion mechanism allowing the con...

In this paper, a hybrid technique of differential quadrature method and Runge-Kutta fourth order method is employed to analyze reaction-diffusion problems. The obtained results are compared with the available analytical ones. Further, a parametric study is introduced to investigate the influence of reaction and diffusion characteristics on behavior of the obtained results. Index Term-Reaction-d...