Solution for Second-Order Differential Equation Using Least Square Method
This paper studies the numerical method for solving differential equations. The continuous least square method (CLSM) is used to obtain the explicit solution for solving ordinary differential equations (ODEs), partial differential equations (PDEs), and fractional differential equations (FDEs), but i...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Tishk International University
2022-06-01
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| Series: | Eurasian Journal of Science and Engineering |
| Subjects: | |
| Online Access: | https://eajse.tiu.edu.iq/index.php/volume-8-issue-1-article-10/ |
| _version_ | 1797759809852801024 |
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| author | Salisu Ibrahim Abdulnasir Isah |
| author_facet | Salisu Ibrahim Abdulnasir Isah |
| author_sort | Salisu Ibrahim |
| collection | DOAJ |
| description | This paper studies the numerical method for solving differential equations. The continuous least square method (CLSM) is used to obtain the explicit solution for solving ordinary differential equations (ODEs), partial differential equations (PDEs), and fractional differential equations (FDEs), but in this work, we consider the explicit results from CLSM approach and applied it on second-order ODEs. Moreover, the L_2 norm is used to obtain the minimum approximation error. The numerical results obtained has a good agreement with the exact solution with minimum approximation error. The explicit results are supported by an example that was treated with Matlab and Matematica 11. |
| first_indexed | 2024-03-12T18:49:48Z |
| format | Article |
| id | doaj.art-943e680121124c9f97f7c2982a4a5cb7 |
| institution | Directory Open Access Journal |
| issn | 2414-5629 2414-5602 |
| language | English |
| last_indexed | 2024-03-12T18:49:48Z |
| publishDate | 2022-06-01 |
| publisher | Tishk International University |
| record_format | Article |
| series | Eurasian Journal of Science and Engineering |
| spelling | doaj.art-943e680121124c9f97f7c2982a4a5cb72023-08-02T07:21:26ZengTishk International UniversityEurasian Journal of Science and Engineering2414-56292414-56022022-06-018111912510.23918/eajse.V8i1p119Solution for Second-Order Differential Equation Using Least Square MethodSalisu Ibrahim0Abdulnasir Isah1Mathematics Education Department, Faculty of Education, Tishk International University, Erbil, IraqMathematics Education Department, Faculty of Education, Tishk International University, Erbil, IraqThis paper studies the numerical method for solving differential equations. The continuous least square method (CLSM) is used to obtain the explicit solution for solving ordinary differential equations (ODEs), partial differential equations (PDEs), and fractional differential equations (FDEs), but in this work, we consider the explicit results from CLSM approach and applied it on second-order ODEs. Moreover, the L_2 norm is used to obtain the minimum approximation error. The numerical results obtained has a good agreement with the exact solution with minimum approximation error. The explicit results are supported by an example that was treated with Matlab and Matematica 11.https://eajse.tiu.edu.iq/index.php/volume-8-issue-1-article-10/differential equationsecond-order differential equationcontinuous least square methodand l_2 norm |
| spellingShingle | Salisu Ibrahim Abdulnasir Isah Solution for Second-Order Differential Equation Using Least Square Method Eurasian Journal of Science and Engineering differential equation second-order differential equation continuous least square method and l_2 norm |
| title | Solution for Second-Order Differential Equation Using Least Square Method |
| title_full | Solution for Second-Order Differential Equation Using Least Square Method |
| title_fullStr | Solution for Second-Order Differential Equation Using Least Square Method |
| title_full_unstemmed | Solution for Second-Order Differential Equation Using Least Square Method |
| title_short | Solution for Second-Order Differential Equation Using Least Square Method |
| title_sort | solution for second order differential equation using least square method |
| topic | differential equation second-order differential equation continuous least square method and l_2 norm |
| url | https://eajse.tiu.edu.iq/index.php/volume-8-issue-1-article-10/ |
| work_keys_str_mv | AT salisuibrahim solutionforsecondorderdifferentialequationusingleastsquaremethod AT abdulnasirisah solutionforsecondorderdifferentialequationusingleastsquaremethod |