### Keywords : Finite Difference Method

##### 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.

##### Numerical Solution of the Problem of Heat Transfer by Convection

Ahmed M. Juma’a; Ashraf S. Aboudi

AL-Rafidain Journal of Computer Sciences and Mathematics, 2006, Volume 3, Issue 2, Pages 71-88
DOI: 10.33899/csmj.2006.164059

In this paper we have presated a heat transfer by convection in rectangular cavity filled with static fluid.  Differentially heated end vertical walls. Two-dimensional motions are assumed. The governing vorticity and energy transport equations are solved by an alternating direction implicit finite- difference method. We transference heat equation into two finite- difference equations. The time interval has been deviled into two equal halves, alternating to compute an intermediate point in the first step and final value at T time. We get by result analysis, that we can reach the steady – state from Un steady –state after some iteration.

##### An Extension Use of ADI Method in the Solution of Biharmonic Equation

Ahmed M. Jassim

AL-Rafidain Journal of Computer Sciences and Mathematics, 2006, Volume 3, Issue 1, Pages 85-94
DOI: 10.33899/csmj.2006.164038

The Biharmonic equation is one of partial differential equations which arise from discussion of some applied sciences such as fluid dynamics. In this paper, we have adopted a numerical method to solve that equation, this method is developed basically from ADI (Alternating- Direction- Implicit) finite difference method which was used in the solution of Laplace equation.