College of Computer Science and Mathematics

Discussion of a Doctorial Dissertation  in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

Solving System of Integral Equations by Using Homotopy Analysis Methods with Genetic Algorithm

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the  University of Mosul on Thursday 12-10-2023

Doctorial Dissertation by student Rasha Fahad Ahmed Abdul Jabar

, under the supervision of Prof. Dr. Abbas Younis Elias Al-Bayati

                   AND       Assist. Prof. Dr. Waleed Mohammed Fathi Al-Hayani

 

Solving systems of linear and nonlinear integral equations is one of the most important and broad numerical and analytical studies, where many methods have been developed to solve these problems either by finding their roots mathematically or by solving them numerically or analytically and improving those solutions to obtain the optimal solution. In this thesis, we proposed a new algorithm to solve these systems, which combines the Genetic Algorithm (GA) and the Homotopy Analysis Method (HAM), where we used the last-mentioned method to solve some types of Integral equations such as the System of Volterra Integral Equations (SVIEs) and the System of Fredholm Integral Equations (SFIEs), and finally, the System of Mixed Volterra-Fredholm Integral Equations (SVFIEs) with the Genetic Algorithm (GA) to get a better approximate solution than using the HAM. Since the HAM contains an auxiliary parameter  that adjusts and controls the convergence region of the series of solutions, then the residual error function is considered as a fitness function for the genetic algorithm, and genetic operations are applied to it to obtain the best  and the best  and apply the HAM again to the system of Integral equations. The new algorithm showed its effectiveness, especially that the obtained results are fully compatible with the h-curves.

The scientific committee included the following members:

prof.Dr. Omar Saber Qasim – Chairman

prof. Dr. Ikhlas Saadullah Ahmed- Member

prof. Dr. Mohanad Ahmed Mahmood – Member

Ass. Prof. Dr. Kais Ismail Ibrahim – member

Ass. Prof.Dr. Saad Fawzi Jasim – Member

prof.Dr. Abbas Younes Elias- Tal Afar University – College of Basic Education – Member and supervisor

Ass. Prof. Dr. Waleed Mohammed Fathi Al-Hayani – Member and supervisor