College of Education for Pure Science

Master Thesis Viva in the College of Education for Pure Science entitled ” Solving fuzzy initial value problems numerically ”

The College of Education for Pure Science, University of Mosul, has done the Master Thesis Viva entitled ” Solving fuzzy initial value problems numerically””,

On Monday, July 17, 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.

The aim of this study, presented by the Master student Marwa Muthanna Yahya Hamid in the Department of Mathematics, is primarily on solving initial value problems for PDEs using numerical methods. Two methods were used: the sixth-order Runge-Kutta method (6RK) and the sixth-order Butcher’s Runge-Kutta method. The application of these methods to PDEs was explained, and a comprehensive error analysis of the proposed algorithm was conducted, helping to understand the accuracy and stability of numerical methods when applied to PDEs.

Numerical results were reviewed, and some linear and nonlinear problems for fuzzy Cauchy problems were solved to demonstrate the application of the algorithm and numerical problem-solving. It can be concluded that this research contributes to the field of fuzzy mathematics by providing a numerical algorithm based on the Runge-Kutta method for solving PDEs. A comprehensive error analysis was presented, and examples were provided to solve fuzzy Cauchy problems.

The Viva committee was chaired by Asst. Prof. Dr. Alan Jalal Abdel Kader / Al-Mustansiriya University /College of Education for Pure Science and the membership of Asst. Prof. Dr. Amal Jassim Mohammed / University of Mosul, College of Education for Pure Science, Lecturer Dr. Hisham Mohamed Khedr, Mosul University / College of Computer Science and Mathematics and under the supervision and membership of Asst. Prof. Dr. Kais Ismail Ibrahim, University of Mosul, College of Education for Pure Science.