Diagonally implicit Runge–Kutta type method for directly solving special fourth-order ordinary differential equations with ill-posed problem of a beam on elastic foundation
In this study, fifth-order and sixth-order diagonally implicit Runge–Kutta type (DIRKT) techniques for solving fourth-order ordinary differential equations (ODEs) are derived which are denoted as DIRKT5 and DIRKT6, respectively. The first method has three and the another one has four identical nonze...
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| Format: | Article |
| Language: | English |
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MDPI
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/77899/ http://psasir.upm.edu.my/id/eprint/77899/1/77899.pdf |
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| author | Ghawadri, Nizam Ghannam Fayez Senu, Norazak Alshareeda, Firas Adel Fawzi Ismail, Fudziah Ibrahim, Zarina Bibi |
| author_facet | Ghawadri, Nizam Ghannam Fayez Senu, Norazak Alshareeda, Firas Adel Fawzi Ismail, Fudziah Ibrahim, Zarina Bibi |
| author_sort | Ghawadri, Nizam Ghannam Fayez |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this study, fifth-order and sixth-order diagonally implicit Runge–Kutta type (DIRKT) techniques for solving fourth-order ordinary differential equations (ODEs) are derived which are denoted as DIRKT5 and DIRKT6, respectively. The first method has three and the another one has four identical nonzero diagonal elements. A set of test problems are applied to validate the methods and numerical results showed that the proposed methods are more efficient in terms of accuracy and number of function evaluations compared to the existing implicit Runge–Kutta (RK) methods. |
| first_indexed | 2025-11-15T12:12:10Z |
| format | Article |
| id | upm-77899 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:12:10Z |
| publishDate | 2019 |
| publisher | MDPI |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-778992020-05-04T17:37:58Z http://psasir.upm.edu.my/id/eprint/77899/ Diagonally implicit Runge–Kutta type method for directly solving special fourth-order ordinary differential equations with ill-posed problem of a beam on elastic foundation Ghawadri, Nizam Ghannam Fayez Senu, Norazak Alshareeda, Firas Adel Fawzi Ismail, Fudziah Ibrahim, Zarina Bibi In this study, fifth-order and sixth-order diagonally implicit Runge–Kutta type (DIRKT) techniques for solving fourth-order ordinary differential equations (ODEs) are derived which are denoted as DIRKT5 and DIRKT6, respectively. The first method has three and the another one has four identical nonzero diagonal elements. A set of test problems are applied to validate the methods and numerical results showed that the proposed methods are more efficient in terms of accuracy and number of function evaluations compared to the existing implicit Runge–Kutta (RK) methods. MDPI 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/77899/1/77899.pdf Ghawadri, Nizam Ghannam Fayez and Senu, Norazak and Alshareeda, Firas Adel Fawzi and Ismail, Fudziah and Ibrahim, Zarina Bibi (2019) Diagonally implicit Runge–Kutta type method for directly solving special fourth-order ordinary differential equations with ill-posed problem of a beam on elastic foundation. Algorithms, 12 (1). art. no. 10. pp. 1-10. ISSN 1999-4893 https://www.mdpi.com/1999-4893/12/1/10 10.3390/a12010010 |
| spellingShingle | Ghawadri, Nizam Ghannam Fayez Senu, Norazak Alshareeda, Firas Adel Fawzi Ismail, Fudziah Ibrahim, Zarina Bibi Diagonally implicit Runge–Kutta type method for directly solving special fourth-order ordinary differential equations with ill-posed problem of a beam on elastic foundation |
| title | Diagonally implicit Runge–Kutta type method for directly solving special fourth-order ordinary differential equations with ill-posed problem of a beam on elastic foundation |
| title_full | Diagonally implicit Runge–Kutta type method for directly solving special fourth-order ordinary differential equations with ill-posed problem of a beam on elastic foundation |
| title_fullStr | Diagonally implicit Runge–Kutta type method for directly solving special fourth-order ordinary differential equations with ill-posed problem of a beam on elastic foundation |
| title_full_unstemmed | Diagonally implicit Runge–Kutta type method for directly solving special fourth-order ordinary differential equations with ill-posed problem of a beam on elastic foundation |
| title_short | Diagonally implicit Runge–Kutta type method for directly solving special fourth-order ordinary differential equations with ill-posed problem of a beam on elastic foundation |
| title_sort | diagonally implicit runge–kutta type method for directly solving special fourth-order ordinary differential equations with ill-posed problem of a beam on elastic foundation |
| url | http://psasir.upm.edu.my/id/eprint/77899/ http://psasir.upm.edu.my/id/eprint/77899/ http://psasir.upm.edu.my/id/eprint/77899/ http://psasir.upm.edu.my/id/eprint/77899/1/77899.pdf |