21 September، 2022
Discussion of a master’s thesis in the Faculty of Computer Science and Mathematics – Department of Mathematics Sciences
Discussion of a master’s thesis in the Faculty of Computer Science and Mathematics – Department of Mathematics Sciences entitled:” Homotopy perturbation Method for Solving Ordinary Differential Equations with Discontinuity and Turning Point “It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Wednesday, corresponding to 9/21/2022
Master’s thesis for student Mohamed Gamal Ahmed Mohamed and under the supervision of Assistant Professor Dr. Walid Mohamed Fathi.
The study dealt with the use of the perturbed homotopy method (HPM) to solve ordinary differential equations of the type of problems with initial values of the first order and of the second order with different patterns of discontinuity, giving the relevant prominent cases for both linear and non-linear for the different cases. Hemotopian perturbative method for solving ODE type problems with boundary values which represent turning points with large and small parameter.The study dealt with showing the high accuracy of the results of the approximate solution compared to the exact solution if it exists, and by making a comparison of the numerical results that apply the turbulent homotopy method with the improvement of the standard turbulent homotopy method using the repetition of the integral equation (IIE) and the numerical solution of the Simpson and trapezoid bases ( Trapezoidal). In addition, the maximum value of the absolute error, the criterion of order 2, the maximum value of the relative error, the maximum value of the residual error, the convergence order estimate at x_i (local) and the total convergence order estimate over the given period were given.
The aim of the thesis is to prove that the turbulent homotopy method is more accurate, convenient and more efficient for solving problems with discontinuity and tipping point.The discussion committee consisted of:-
Assistant Professor Dr. Qais Ismail Ibrahim – University of Mosul – College of Education for Pure Sciences – President
Assistant Professor Dr. Muhannad Ahmed Mahmoud – University of Kirkuk – College of Science.
Assistant Professor Dr. Ahmed Intisar Ghaith – Member
Assistant Professor Dr. Walid Mohamed Fathi – member and supervisor.
