On two derivative Runge-Kutta type methods for solving u''' = f (x, u(x)) with application to thin film flow problem
A class of explicit Runge–Kutta type methods with the involvement of fourth derivative, denoted as two-derivative Runge–Kutta type (TDRKT) methods, are proposed and investigated for solving a special class of third-order ordinary differential equations in the form u′′′(x)=f(x,u(x)) . In this paper,...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Multidisciplinary Digital Publishing Institute
2020
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| Online Access: | http://psasir.upm.edu.my/id/eprint/86978/ http://psasir.upm.edu.my/id/eprint/86978/1/On%20two%20derivative%20Runge.pdf |
| _version_ | 1848860334968799232 |
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| author | Lee, Khai Chien Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal |
| author_facet | Lee, Khai Chien Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal |
| author_sort | Lee, Khai Chien |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A class of explicit Runge–Kutta type methods with the involvement of fourth derivative, denoted as two-derivative Runge–Kutta type (TDRKT) methods, are proposed and investigated for solving a special class of third-order ordinary differential equations in the form u′′′(x)=f(x,u(x)) . In this paper, two stages with algebraic order four and three stages with algebraic order five are presented. The derivation of TDRKT methods involves single third derivative and multiple evaluations of fourth derivative for every step. Stability property of the methods are analysed. Accuracy and efficiency of the new methods are exhibited through numerical experiments. |
| first_indexed | 2025-11-15T12:43:36Z |
| format | Article |
| id | upm-86978 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:43:36Z |
| publishDate | 2020 |
| publisher | Multidisciplinary Digital Publishing Institute |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-869782022-09-05T03:36:28Z http://psasir.upm.edu.my/id/eprint/86978/ On two derivative Runge-Kutta type methods for solving u''' = f (x, u(x)) with application to thin film flow problem Lee, Khai Chien Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal A class of explicit Runge–Kutta type methods with the involvement of fourth derivative, denoted as two-derivative Runge–Kutta type (TDRKT) methods, are proposed and investigated for solving a special class of third-order ordinary differential equations in the form u′′′(x)=f(x,u(x)) . In this paper, two stages with algebraic order four and three stages with algebraic order five are presented. The derivation of TDRKT methods involves single third derivative and multiple evaluations of fourth derivative for every step. Stability property of the methods are analysed. Accuracy and efficiency of the new methods are exhibited through numerical experiments. Multidisciplinary Digital Publishing Institute 2020-06-02 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/86978/1/On%20two%20derivative%20Runge.pdf Lee, Khai Chien and Senu, Norazak and Ahmadian, Ali and Ibrahim, Siti Nur Iqmal (2020) On two derivative Runge-Kutta type methods for solving u''' = f (x, u(x)) with application to thin film flow problem. Symmetry-Basel, 12 (6). pp. 1-22. ISSN 2073-8994 https://www.mdpi.com/2073-8994/12/6/924 10.3390/sym12060924 |
| spellingShingle | Lee, Khai Chien Senu, Norazak Ahmadian, Ali Ibrahim, Siti Nur Iqmal On two derivative Runge-Kutta type methods for solving u''' = f (x, u(x)) with application to thin film flow problem |
| title | On two derivative Runge-Kutta type methods for solving u''' = f (x, u(x)) with application to thin film flow problem |
| title_full | On two derivative Runge-Kutta type methods for solving u''' = f (x, u(x)) with application to thin film flow problem |
| title_fullStr | On two derivative Runge-Kutta type methods for solving u''' = f (x, u(x)) with application to thin film flow problem |
| title_full_unstemmed | On two derivative Runge-Kutta type methods for solving u''' = f (x, u(x)) with application to thin film flow problem |
| title_short | On two derivative Runge-Kutta type methods for solving u''' = f (x, u(x)) with application to thin film flow problem |
| title_sort | on two derivative runge-kutta type methods for solving u''' = f (x, u(x)) with application to thin film flow problem |
| url | http://psasir.upm.edu.my/id/eprint/86978/ http://psasir.upm.edu.my/id/eprint/86978/ http://psasir.upm.edu.my/id/eprint/86978/ http://psasir.upm.edu.my/id/eprint/86978/1/On%20two%20derivative%20Runge.pdf |