Discussion of the doctoral thesis at the College of Computer Science and Mathematics, Department of Mathematics, entitled:

“Numerical and Approximate Methods for Solving Nonlinear Cyber-Physical Medical Systems”

supervised by Prof. Dr. Ahmed Farooq Qasim.

The Thesis Addressed

This thesis aims to develop approximate and numerical methods for solving systems of nonlinear partial differential equations, with the objective of improving solution accuracy, accelerating convergence, and enhancing computational efficiency.

The thesis develops a hybrid approach that combines double and triple Laplace transforms with the Accelerated Adomian Decomposition Method. This approach provides more accurate and well-structured approximate solutions, particularly when dealing with nonlinear terms and boundary conditions.

The finite-volume method was also improved by integrating it with quadratic spectral reconstruction, Spectral–T2. This development improves the calculation of values at cell faces, reduces numerical errors, and preserves the conservative structure of the finite-volume method.

Furthermore, a new method combining the two-point Taylor expansion with the Adomian Decomposition Method was proposed. This method uses information from two points within the spatial domain instead of relying on a single expansion point, thereby providing a more flexible and accurate approximation.

The proposed methods were theoretically supported by establishing convergence, existence, uniqueness, and stability under specific mathematical conditions. They were also applied to mathematical test problems with exact solutions and to a spatiotemporal medical system describing the transport of two drugs and their effects on cellular variables. Numerical comparisons and graphical results demonstrated reduced errors and the practical superiority of the developed methods.

Finally, conclusions based on theoretical analysis and numerical comparisons were presented, together with recommendations for extending the proposed methods to more complex nonlinear systems and medical models.

The Discussion Committee Consisted of

• Prof. Dr. Ikhlas Saadallah Ahmed — Chair
• Prof. Dr. Abdulghafour Mohammed Amin — Member
• Asst. Prof. Dr. Badran Jasim Salim — Member
• Asst. Prof. Dr. Mohammed Omar Shaaban — Member
• Asst. Prof. Dr. Ahmed Shawqi Jabir — Member
• Prof. Dr. Ahmed Farooq Qasim — Member and Supervisor