College of Education for Pure Science

Master Thesis Viva in the College of Education for Pure Science entitled ” Hybridization of the homotopy analysis method with the ant algorithm to solve systems of differential equations ”

The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled ” Hybridization of the homotopy analysis method with the ant algorithm to solve systems of differential equations””,

On Monday, September 11, 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 Marwa Abdulghafor Mohammed Amin Khudhur in the Department of Mathematics, the proposed method (HAM-ACO) was used to solve systems of differential equations, as the Homotopy Analysis Method (HAM) was hybridized with the Ant Colony Optimization algorithm (ACO)), by means of Dependence on the final series resulting from the Homotopy Analysis Method (HAM), which represents the fitness function of the Ant Colony Optimization algorithm (ACO), where the algorithm works to find the best values for the parameters from the set of possible solutions, by creating an initial community consisting of several individuals and each individual It consists of several random values that are determined by the size of the parameters, and by applying the Ant Colony Optimization algorithm (ACO), we find the remaining communities that include the best values of the parameters, as this proposed method (HAM-ACO) works to converge the results from the exact solution by calculating the maximum value of error (Maximum Absolute Error (MAE)) and Mean Square Error (MSE)) and graphs. Software applications were also used to solve the applied examples in this thesis by Maple program.

The Viva committee was chaired by Asst. Prof. Dr. Alan Jalal Abdulqadir / Al-Mustansirya University /College of Education and the membership of Prof. Dr. Ahmed Farouk Qasim / University of Mosul /College of Computer Science and Mathematics , Lecturer Dr. Azzam Salahuddin Younus / University of Mosul/ College of Education for Pure Science and under the supervision and membership of both Asst. Prof. Dr. Kais Ismail Ibraheem / University of Mosul, College of Education for Pure Science and Asst. Prof. Dr. Ahmed Entesar Ghatheeth/ University of Mosul /College of Computer Science and Mathematics