### Main Subjects : Numerical Analysis

##### Applied Sumudu Transform with Adomian Decomposition Method to the Coupled Drinfeld–Sokolov–Wilson System

Abdulghafor M. Al-Rozbayani; Ammar H. Ali

AL-Rafidain Journal of Computer Sciences and Mathematics, 2021, Volume 15, Issue 2, Pages 139-147
DOI: 10.33899/csmj.2021.170017

In this paper, we studied and applied a modern numerical method, which is combining Sumudu transform with Adomian decomposition Method to obtain approximate solutions of the nonlinear the Coupled Drinfeld– Sokolov–Wilson (DSW) system. Positive and negative values of the variable x and various values of the variable t were taken with the initial conditions of the system as well as the values of the parameters . The efficiency of the method was verified, as the results obtained were compared with the accurate solution of the system. We noticed that the results are very accurate and the effectiveness of the method was confirmed.

##### Numerical Solution of Electromagnetic Problem MHD in a Polar Coordinates

Ahmed M.J. Jassim; Ahmed S.J. Amen

AL-Rafidain Journal of Computer Sciences and Mathematics, 2021, Volume 15, Issue 1, Pages 23-34
DOI: 10.33899/csmj.2021.168257

In this paper, we studied a flow of fluid in a pipe under the effect of electromagnetic field in a polar coordinate, be done build a mathematical model which  represented by system of  two dimensional non-linear partial differential equations and we solved it by using  Alternating Directions Implicit method (ADI) which is one of the finite differences method, and from the numerical solution indicated the behavior of  temperature distribution inside the pipe, be done explication the influence of  Rayleigh number and Prandtl number as well as the influence of Eckert number upon the behavior of  temperature distribution are also done through the energy equation  in polar coordinate, we arrived to steady state from unsteady state, we find the behavior of fluid flow inside the pipe  and also we studied the influence of  Hartmann  number  upon the behavior of  fluid flow in pipe and all this done through the motion equation in polar coordinate.

##### The Homotopy Analysis Method in Turning Point Problems

Rasha F. Ahmed; Waleed M. Al-Hayani

AL-Rafidain Journal of Computer Sciences and Mathematics, 2020, Volume 14, Issue 1, Pages 51-65
DOI: 10.33899/csmj.2020.164676

In this paper, we used the homotopy analysis method to ordinary differential equations of type boundary value problems with a parameter representing turning points."To show the high accuracy of the solution results, we compare the numerical results applying the standard homotopy analysis method with the integral equation and the numerical solution of the Simpson and Trapezoidal rules."Also, we give the estimated order of convergence (local) and the global estimated order of convergence along the interval.

##### Stability Analysis of Fisher Equation Using Numerical Galerkin Techniques

Saad A. Manna; Ahmed F. Qassem

AL-Rafidain Journal of Computer Sciences and Mathematics, 2006, Volume 3, Issue 2, Pages 29-42
DOI: 10.33899/csmj.2006.164057

We studied the stability of the steady state solutions for Fisher Equation in two cases, the First one with constant amplitude and we show that the steady state solution is always stable under any condition, but the other two solutions and  are conditionally stable.
In the Second case, we studied the steady state solutions for various amplitude by using two Methods. The First is analytically by direct Method and the second is numerical method using Galerkin technique which shows the same results, that is the steady state solution  is always stable under any conditions, but the other two solutions and are conditionally stable.

##### Numerical Analysis of Fisher Equation

Saad A. Manna; Ahmed F. Qassim

AL-Rafidain Journal of Computer Sciences and Mathematics, 2006, Volume 3, Issue 1, Pages 85-100
DOI: 10.33899/csmj.2006.164046

The Fisher Equation had been solved numerically by using two Methods of Finite Differences Methods. The First is Explicit Scheme Method and the Second is Crank–Nicholson Method. A Comparison had been made between these two methods and we find that the Crank–Nicholson Method converges towards saturation state u=1 faster than the Explicit Scheme Method (Table 1). Also the numerical stability for both Methods had been made, the Explicit Scheme Method is conditionally stable and the condition is , while Crank–Nicholson Method has the condition for step size, but time step  is unconditionally stable.