College of Education for Pure Science

Master Thesis Viva in the College of Education for Pure Science entitled ” Solving Fredholm and Volterra Integral Equations by Particle Swarm Optimization and Cultural Algorithm Using Padé Approximants ”

The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled ” Solving Fredholm and Volterra Integral Equations by Particle Swarm Optimization and Cultural Algorithm Using Padé Approximants””,

On Sunday, July 30, 2023, the College staff including the respected Dean of the College, Assistant Professor Dr. Qais Ismail Ibrahim, the Honorable Scientific Associate and Administrative Associate, the Honorable Head of the Department of Mathematics, and a number of the college’s teachers were attended the viva.

In this study, presented by the Master student Israa Ibrahim Mohammed Karmoosh in the Department of Mathematics, An algorithm has been proposed to solve the linear and nonlinear Volterra and Fredholm integral equations of second kind by converting them into an unrestricted optimization problem. This algorithm includes Particle Swarm Optimization (PSO) and Cultural Algorithm (CA) based on Padé Expansion Approximation, since many solutions of linear and nonlinear integral equations contain different formulas, therefore, Padé expansion which is represented as a fractional expansion was used to obtain accurate results. The Fitness Function(FF) was used as a quantitative criterion to determine the accuracy of approximate solutions through the Discrete Least Square Weighted Function (DLSWF).

The two algorithms (Particle Swarm Optimization Algorithm and Cultural Algorithm) were applied to a set of Fredholm and Volterra integral equations of the second kind, the application of these two algorithms provide high accuracy results. These results demonstrate the ability of the proposed algorithm to solve the linear and nonlinear Fredholm and Volterra integral equations of the second kind.

The Viva committee was chaired by Prof. Dr. Akram Hassan Mahmood / Mosul University /College of Education for Pure Science and the membership of Asst. Prof. Dr. Ammar Isam Edress / Technical College of Petroleum and Minerals- Zakh/ Duhok Polytechnic University, Asst. Prof. Dr. Mohammed Abdulrazaq Alkahya, Mosul University / College of Education for Pure Science and under the supervision and membership of Lecturer Dr. Azzam Salahuddin Younus, University of Mosul, College of Education for Pure Science.