مشروع البحث: Using Abaoub-Shkheam Transform for Solving a Nonlinear Volterra Integral Equation of the First Kind
| dc.contributor.advisor | علي الحراري | |
| dc.date.accessioned | 2024-11-25T10:07:35Z | |
| dc.date.available | 2024-11-25T10:07:35Z | |
| dc.description | It is known that integral equations are of great importance, whether in research mathematics or applied, this importance comes from its direct connection to a large number of branches of mathematics, engineering, and physics, and it has contributed to solving many chemical and physical problems. The concept of integral equations appeared since the time of Riemann and was strengthened in the seventeenth century at the hands of scientists such as Poincae and Hilbert, integral equations research was developed by scientists such as Volterra and Fredholm. The Volterra and Fredholm equations are considered the most important and widely used. These equations are classified into linear and nonlinear. In this thesis, we focus on the nonlinear Volterra integral equations. | |
| dc.description.abstract | The main goal of this thesis is to study integral equations in which the limits of integration are at least one limit is a variable, and the unknown function occurs under the integral sign only, these equations are named nonlinear Volterra integral equations of the first kind. In this study, we will prove the existence and uniqueness of solutions by successive approximations after converting the equation to the second kind. We will also use the Abaoub-Shkheam transform to solve a nonlinear Volterra integral equation of the first kind. This technique will be illustrated with some numerical applications. | |
| dc.identifier | 2323 | |
| dc.identifier.uri | https://dspace.academy.edu.ly/handle/123456789/314 | |
| dc.subject | Using Abaoub-Shkheam Transform for Solving a Nonlinear Volterra Integral Equation of the First Kind | |
| dc.title | Using Abaoub-Shkheam Transform for Solving a Nonlinear Volterra Integral Equation of the First Kind | |
| dspace.entity.type | Project | |
| project.endDate | 2023 | |
| project.funder.name | علوم الرياضيات | |
| project.investigator | اسماء المبروك محمد | |
| project.startDate | 2022 |