College of Education for Pure Science

Master Thesis Viva in the College of Education for Pure Science entitled ” Solving Systems of Ordinary Differential Equations Using Particle Swarm Optimization and Genetic algorithm Based on Padé Approximant “The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled ” Solving Systems of Ordinary Differential Equations Using Particle Swarm Optimization and Genetic algorithm Based on Padé Approximant “,On Wednesday, August 24, 2022, 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 Reham Haitham Salim Alazzawi in the Department of Mathematics, the systems of Ordinary Differential Equations (SODEs) were transformed into constrained optimization problems to find their approximate solutions. An algorithm is proposed by applying particle swarm optimization (PSO) and the genetic algorithm (Genetic Algorithm (GA) based on the Padé expansion approximation (PEA). Since many solutions of linear and nonlinear SODEs have different formulas, Padé approximation expansion was used as it is a fractional expansion. This leads to obtain results with higher accuracy than other expansions.A quantitative criterion represented by the Fitness Function (FF)) is used for the purpose of determining the accuracy of approximate solutions by adding a Penalty Function (PF) to the Discrete Least Square Weighted Function (DLSWF)).Particle swarm optimization (PSO) and the genetic algorithm (Genetic Algorithm (GA) was applied to a set of SODEs. It was found that the results were accurate and close to the exact solution of SODEs in most of the tests. These results demonstrate the ability of the proposed algorithm to solve linear and nonlinear ODE systems with initial or boundary conditions.The Viva committee was chaired by Prof. Dr. Alaa Abdulraheem Ahmed from University of Mosul, College of Education for Pure Science and the membership of Asst. Prof. Dr. Ahmed Entesar Ghitheeth/University of Mosul, College of Computer Science and Mathematics, Asst. Prof. Dr. Muayyad Mahmood Khalil/ Tikrit University /College of Education for Pure Sciences and under the supervision and membership of Lect. Dr. Azzam Salahuddin Younus, University of Mosul, College of Education for Pure Science.