Keywords : reaction-diffusion system


Fourier Stability Analysis of Two Finite Element Schemes for Reaction-Diffusion System with Fast Reversible Reaction

Ann Jalal; Mohammed O. Al-Amr

AL-Rafidain Journal of Computer Sciences and Mathematics, 2013, Volume 10, Issue 3, Pages 117-128
DOI: 10.33899/csmj.2013.163531

In this paper, the stability analysis is performed on two Galerkin finite element schemes for solving reaction-diffusion system with fast reversible reaction.  Fourier (Von Neumann) method is implemented to propose time-step criteria for the consistent and the lumped schemes with four popular choices for . We have found that the two schemes are unconditionally stable when , while the consistent scheme is stable under the conditions  and  when . Also, the lumped scheme is stable under the conditions  and  when .
 
 

Numerical Solution of a Reaction-Diffusion System with Fast Reversible Reaction by Using Adomian’s Decomposition Method and He’s Variational Iteration Method

Ann Jalal; Mohammed O. Al-Amr

AL-Rafidain Journal of Computer Sciences and Mathematics, 2012, Volume 9, Issue 2, Pages 243-257
DOI: 10.33899/csmj.2012.163715

In this paper, the approximate solution of a reaction-diffusion system with fast reversible reaction is obtained by using Adomian decomposition method (ADM) and variational iteration method (VIM) which are two powerful methods that were recently developed. The VIM requires the evaluation of the Lagrange multiplier, whereas ADM requires the evaluation of the Adomian polynomials. The behavior of the approximate solutions and the effects of different values of  are shown graphically.
 

Numerical Solution for Linear Parabolic Reaction-Double Diffusivity System using the Operational Matrices of the Haar Wavelets Method

Ahmed F. Qasem

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 1, Pages 177-195
DOI: 10.33899/csmj.2008.163958

We are using the operational matrices of the Haar wavelets method for solving linear parabolic reaction-diffusion system with double diffusivity. A numerical method based on the Haar wavelets approach which has the property  , we compared this result with the exact solution for reaction-diffusion system, we found that high accuracy of the results in this method in the solution double diffusivity system even in the case of a small number of grid points is used. However, the computation is simple because consists of the matrices which can be programmed by Matlab language, thes matrices which we got  of the numerical solution are representing all time steps while the finite difference method and finite elements method need the iteration to get the needed time step, they are complicated and time-consuming.