2 November، 2023

Nibal Sabah Abdulrhman’s Doctorial Thesis ,from Mathematics Department, on Final Defense

Discussion of a Doctorial Dissertation in the College of Computer Science and Mathematics – Department of Mathematics Sciences entitled:

**Local Linearization Method for Some Stochastic Differential Equation with Application**

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In continuation of the scientific research movement and with the follow-up and presence of the Dean of the College of Computer Science and Mathematics

**Prof. Dr. Duha Bashir Abdullah The Esteemed**

It was discussed in the discussion room at the Faculty of Computer Science and Mathematics at the University of Mosul on Thursday **2-11-2023**

Doctorial Dissertation by student **Nibal Sabah Abdulrhman**

, under the supervision of **Prof. Dr.** **Abdulghafoor Jasim Salim**** **

This thesis included a study of nonlinear stochastic differential equations and their analytical and approximate solutions. The analytical methods were or represented in several ways, either directly by using the integrative factor by using the transformation to the linear formula after testing whether it is reducible. if it is irreducible, the solution is found by the method of the integral factor for nonlinear equations. if it is reducible, then the transformation methods were used depending on the formula Integral and comparative Ito with the general linear formula of stochastic differential equations and compared with Ito’s integral formula in order to find the appropriate transformation function U(t,x) For the deterministic limit after deleting the terms that have exponents greater than one to convert to linear, which is equivalent to (drift function) in the stochastic differential equation. In this study, we tried to use Ito’s integrative formula for both limits (the deterministic and the stochastic) which is equivalent to f(t, y) the deviation function and g(t, y) the diffusion function. In order to make a comparison between the obtained solution to the stochastic differential equations using the direct methods or the approximation methods, we tried to use the numerical methods (Euler-Maruyama and Milstein’s method). The thesis consists of six chapters.

The scientific committee included the following members:

prof.Dr. Hasan Hussein Ibrahim – Chairman

prof. Dr. Akram Hassan Mohammad – Member

Ass.prof. Dr. Ahmed Mohammed Juma’a – Member

Ass. Prof. Saad Fawzi Jasim – member

Ass. Prof. Dr. Ahmed Farouk Qasim – Member

prof.Dr. Abdulghafoor Jasim Salim – Member and supervisor

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