Exponentially Fitted Diagonally Implicit EDITRK Method for Solving ODEs
This paper derives the EDITRK4 technique, which is an exponentially fitted diagonally implicit RK method for solving ODEs . This approach is intended to integrate exactly initial value problems (IVPs), their solutions consist of linear combinations of the group functions and for exponentially fitt...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Baghdad
2023-01-01
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| Series: | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| Subjects: | |
| Online Access: | https://jih.uobaghdad.edu.iq/index.php/j/article/view/2883 |
| _version_ | 1797937687618912256 |
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| author | Firas A. Fawzi Nour W. Jaleel |
| author_facet | Firas A. Fawzi Nour W. Jaleel |
| author_sort | Firas A. Fawzi |
| collection | DOAJ |
| description | This paper derives the EDITRK4 technique, which is an exponentially fitted diagonally implicit RK method for solving ODEs . This approach is intended to integrate exactly initial value problems (IVPs), their solutions consist of linear combinations of the group functions and for exponentially fitting problems, with being the problem’s major frequency utilized to improve the precision of the method. The modified method EDITRK4 is a new three-stage fourth-order exponentially-fitted diagonally implicit approach for solving IVPs with functions that are exponential as solutions. Different forms of -order ODEs must be derived using the modified system, and when the same issue is reduced to a framework of equations that can be solved using conventional RK approaches, numerical comparisons must be done. The findings show that the novel approach is more efficacious than previously published methods. |
| first_indexed | 2024-04-10T18:48:13Z |
| format | Article |
| id | doaj.art-6eb5d050439a41d1a45ce865ee389091 |
| institution | Directory Open Access Journal |
| issn | 1609-4042 2521-3407 |
| language | English |
| last_indexed | 2024-04-10T18:48:13Z |
| publishDate | 2023-01-01 |
| publisher | University of Baghdad |
| record_format | Article |
| series | Ibn Al-Haitham Journal for Pure and Applied Sciences |
| spelling | doaj.art-6eb5d050439a41d1a45ce865ee3890912023-02-01T08:52:15ZengUniversity of BaghdadIbn Al-Haitham Journal for Pure and Applied Sciences1609-40422521-34072023-01-0136138939910.30526/36.1.28834254Exponentially Fitted Diagonally Implicit EDITRK Method for Solving ODEsFiras A. Fawzi0Nour W. Jaleel1Department of Mathematics, Faculty of Computer Science and Mathematics, Tikrit University, Sallah AL-Deen, IRAQDepartment of Mathematics,Faculty of Computer Science and Mathematics ,University of TikritThis paper derives the EDITRK4 technique, which is an exponentially fitted diagonally implicit RK method for solving ODEs . This approach is intended to integrate exactly initial value problems (IVPs), their solutions consist of linear combinations of the group functions and for exponentially fitting problems, with being the problem’s major frequency utilized to improve the precision of the method. The modified method EDITRK4 is a new three-stage fourth-order exponentially-fitted diagonally implicit approach for solving IVPs with functions that are exponential as solutions. Different forms of -order ODEs must be derived using the modified system, and when the same issue is reduced to a framework of equations that can be solved using conventional RK approaches, numerical comparisons must be done. The findings show that the novel approach is more efficacious than previously published methods.https://jih.uobaghdad.edu.iq/index.php/j/article/view/2883numerical methods exponentially fittedordinary differential equationsdiagonal implicit type runge kutta methods |
| spellingShingle | Firas A. Fawzi Nour W. Jaleel Exponentially Fitted Diagonally Implicit EDITRK Method for Solving ODEs Ibn Al-Haitham Journal for Pure and Applied Sciences numerical methods exponentially fitted ordinary differential equations diagonal implicit type runge kutta methods |
| title | Exponentially Fitted Diagonally Implicit EDITRK Method for Solving ODEs |
| title_full | Exponentially Fitted Diagonally Implicit EDITRK Method for Solving ODEs |
| title_fullStr | Exponentially Fitted Diagonally Implicit EDITRK Method for Solving ODEs |
| title_full_unstemmed | Exponentially Fitted Diagonally Implicit EDITRK Method for Solving ODEs |
| title_short | Exponentially Fitted Diagonally Implicit EDITRK Method for Solving ODEs |
| title_sort | exponentially fitted diagonally implicit editrk method for solving odes |
| topic | numerical methods exponentially fitted ordinary differential equations diagonal implicit type runge kutta methods |
| url | https://jih.uobaghdad.edu.iq/index.php/j/article/view/2883 |
| work_keys_str_mv | AT firasafawzi exponentiallyfitteddiagonallyimpliciteditrkmethodforsolvingodes AT nourwjaleel exponentiallyfitteddiagonallyimpliciteditrkmethodforsolvingodes |