1 October، 2023
Ali Abdulqader Mustafa Majeed’s Doctorial Dissertation ,from Computer Science Department, on Final Defense
Discussion of a Doctorial Dissertation in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:
“ Solving Partial Differential Equations by Using Variational Iteration 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 Sunday 1-10-2023
Doctorial Dissertation by student Ali Abdulqader Mustafa Majeed
, under the supervision of Assist. Prof. Dr. Waleed Mohammed Fathi Al-Hayani
The variational iteration method (VIM) and modified variational iteration method (MVIM) were used in this thesis to solve non-linear partial differential equations (NLPDEs), including the two-dimensional reaction-diffusion Brusselator (RDB) system, the two-dimensional Burger’s equation, the one-dimensional Schrödinger-KdV equation, and the generalized Hirota-Satsuma KdV system.
The MVIM has an auxiliary parameter that allows one to easily establish and regulate the convergence zone of the solution series, and this method’s convergence has been theoretically shown.
The genetic algorithm (GA) was used for developing the results for VIM and MVIM by finding the best value for parameter and utilizing the residual error (MRE) or mean square error (MSE) as the GA’s fitness function.
Finally, the results obtained show that the suggested approaches are very accurate, practical, and effective for solving NLPDEs and can be used to solve other equations.
The scientific committee included the following members:
- Dr. Wafaa Muhi Aldin Taha – Chairman .
- Prof. Dr. Saad Fawzi Jasim- Member.
- Prof. Dr. Abdulghafor Mohammed Amin – Member.
- Prof. Dr. Ahmed Farouk Qasim – Member.
- Prof. Dr. Mohammed Wajed Mohammed Ali – Member
- Prof. Dr. Waleed Mohammed Fathi Al-Hayani – Member and Supervisor
