31 July، 2024
Master’s thesis by student Mohamed Hazem Jassim Mohamed
Discussion of a master’s thesis in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:
“ Combined Variational Iteration Method and Laplace Transform for Solving Singular IVPs of Lane-Emden Type Differential Equations“
In continuation of the scientific research movement and with the follow-up and presence of the Dean of the College of Computer Science and Mathematics
Prof. Dr. Duha Bashir Abdullah The esteemed
It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Wednesday 31-7-2024
Master’s thesis by student Mohamed Hazem Jassim Mohamed, under
the supervision of Assist. Prof. Dr. Waleed Mohammed Fathi Al-Hayani.
The dissertation addresses the combined effects of the method of Variational Iteration Method and the Laplace Transform (LTVIM) for solving singular IVPs and BVPs of Lane-Emden and Emden-Fowler type ODEs and PDEs for linear and non-linear, with the optimization of the obtained solution and increasing its accuracy by using the Padé approximants method of an order [N/M] (PA[N/M]) on the last obtained iteration. It also shows how to deal with the singular point and its treatment, in addition to showing how to extract the value of Lagrange Multiplier and its difference in each order of ODEs and PDEs, whether it is the equation of Heat or the equation of Wave. The solution produced by this method with the least number of iterations shows its effectiveness.
The absolute errors between the exact solution with the suggested method (LTVIM), and the exact solution with the Padé approximants of order [N/M] are also calculated to see its effectiveness. The dissertation offers a thorough examination of the LTVIM and its application in solving differential equations of types of Lane-Emden and Emden-Fowler
The scientific committee included the following members :
- Prof. Dr. Thair Younis Thanoon – Chairman
2- Assist. Prof. Dr. Ahmed Mohammed Jumah- Member.
3- Assist. Prof. Dr. Mohammed Omar Shaaban – Member .
4- Assist. Prof. Dr. Waleed Mohammed Fathi Al-Hayani- Member and supervisor .
