Explicit Solution of First-Order Differential Equation Using Aitken’s and Newton’s Interpolation Methods
The struggle to find the analytic solution of several differential equations leads to several issues like difficulty in finding solutions, singularities, convergent issues, and stability. Because of these problems, most of the researchers come up with explicit approaches such as the Runge Kutta meth...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Tishk International University
2023-02-01
|
| Series: | Eurasian Journal of Science and Engineering |
| Subjects: | |
| Online Access: | https://eajse.tiu.edu.iq/index.php/volume-9-issue-1-article-4/ |
| _version_ | 1797894186423287808 |
|---|---|
| author | Salisu Ibrahim |
| author_facet | Salisu Ibrahim |
| author_sort | Salisu Ibrahim |
| collection | DOAJ |
| description | The struggle to find the analytic solution of several differential equations leads to several issues like difficulty in finding solutions, singularities, convergent issues, and stability. Because of these problems, most of the researchers come up with explicit approaches such as the Runge Kutta method, Euler’s method, and Taylor’s polynomial method for finding numerical solutions to the ordinary differential equation. In this work, we combine both the Aitken methods and Newton’s interpolation method (NIM) to solve first-order differential equations. The numerical results obtained provide minimal error. The result is supported by solving an example. |
| first_indexed | 2024-04-10T07:04:50Z |
| format | Article |
| id | doaj.art-4d23b69ef1a84acda19306bad42d35fd |
| institution | Directory Open Access Journal |
| issn | 2414-5629 2414-5602 |
| language | English |
| last_indexed | 2024-04-10T07:04:50Z |
| publishDate | 2023-02-01 |
| publisher | Tishk International University |
| record_format | Article |
| series | Eurasian Journal of Science and Engineering |
| spelling | doaj.art-4d23b69ef1a84acda19306bad42d35fd2023-02-27T08:45:52ZengTishk International UniversityEurasian Journal of Science and Engineering2414-56292414-56022023-02-0191465610.23918/eajse.v9i1p46Explicit Solution of First-Order Differential Equation Using Aitken’s and Newton’s Interpolation MethodsSalisu Ibrahim 0Mathematics Education Departments, Faculty of Education, Tishk International University-Erbil, Kurdistan Region, IraqThe struggle to find the analytic solution of several differential equations leads to several issues like difficulty in finding solutions, singularities, convergent issues, and stability. Because of these problems, most of the researchers come up with explicit approaches such as the Runge Kutta method, Euler’s method, and Taylor’s polynomial method for finding numerical solutions to the ordinary differential equation. In this work, we combine both the Aitken methods and Newton’s interpolation method (NIM) to solve first-order differential equations. The numerical results obtained provide minimal error. The result is supported by solving an example.https://eajse.tiu.edu.iq/index.php/volume-9-issue-1-article-4/ordinary differential equationaitken’s methodnewton interpolation polynomialnumerical approximation |
| spellingShingle | Salisu Ibrahim Explicit Solution of First-Order Differential Equation Using Aitken’s and Newton’s Interpolation Methods Eurasian Journal of Science and Engineering ordinary differential equation aitken’s method newton interpolation polynomial numerical approximation |
| title | Explicit Solution of First-Order Differential Equation Using Aitken’s and Newton’s Interpolation Methods |
| title_full | Explicit Solution of First-Order Differential Equation Using Aitken’s and Newton’s Interpolation Methods |
| title_fullStr | Explicit Solution of First-Order Differential Equation Using Aitken’s and Newton’s Interpolation Methods |
| title_full_unstemmed | Explicit Solution of First-Order Differential Equation Using Aitken’s and Newton’s Interpolation Methods |
| title_short | Explicit Solution of First-Order Differential Equation Using Aitken’s and Newton’s Interpolation Methods |
| title_sort | explicit solution of first order differential equation using aitken s and newton s interpolation methods |
| topic | ordinary differential equation aitken’s method newton interpolation polynomial numerical approximation |
| url | https://eajse.tiu.edu.iq/index.php/volume-9-issue-1-article-4/ |
| work_keys_str_mv | AT salisuibrahim explicitsolutionoffirstorderdifferentialequationusingaitkensandnewtonsinterpolationmethods |