In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...

Class of cellular automata (CA) for modeling reaction diffusion systems has been presented. The construction of the CA is general enough to be applicable to large class of reaction diffusion equation s. Tne automata are based on running average procedure and on probabilistic table look up to implement diffusion reactions. The evolution of probabilistic CA simulates a spatially distributed proce...

systems in which reaction terms are coupled to diffusion and advection transports arise in awide range of chemical engineering applications, physics, biology and environmental. in these cases, thecomponents of the unknown can denote concentrations or population sizes which represent quantities andthey need to remain positive. classical finite difference schemes may produce numerical drawbacks s...