Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus
Theory and applications of non-Newtonian calculus have been evolving rapidly over the recent years. As numerical methods have a wide range of applications in science and engineering, the idea of the design of such numerical methods based on non-Newtonian calculus is self-evident. In this paper, the...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2015/594685 |
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| _version_ | 1832558193333501952 |
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| author | Uğur Kadak Muharrem Özlük |
| author_facet | Uğur Kadak Muharrem Özlük |
| author_sort | Uğur Kadak |
| collection | DOAJ |
| description | Theory and applications of non-Newtonian calculus have been evolving rapidly over the recent years. As numerical methods have a wide range of applications in science and engineering, the idea of the design of such numerical methods based on non-Newtonian calculus is self-evident. In this paper, the well-known Runge-Kutta method for ordinary differential equations is developed in the frameworks of non-Newtonian calculus given in generalized form and then tested for different generating functions. The efficiency of the proposed non-Newtonian Euler and Runge-Kutta methods is exposed by examples, and the results are compared with the exact solutions. |
| format | Article |
| id | doaj-art-ab4cb786c46849cab5123a8e93ef2a97 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-ab4cb786c46849cab5123a8e93ef2a972025-02-03T01:33:01ZengWileyAbstract and Applied Analysis1085-33751687-04092015-01-01201510.1155/2015/594685594685Generalized Runge-Kutta Method with respect to the Non-Newtonian CalculusUğur Kadak0Muharrem Özlük1Department of Mathematics, Faculty of Sciences, Gazi University, 06100 Ankara, TurkeyDepartment of Mathematics, Faculty of Sciences and Arts, Batman University, 72060 Batman, TurkeyTheory and applications of non-Newtonian calculus have been evolving rapidly over the recent years. As numerical methods have a wide range of applications in science and engineering, the idea of the design of such numerical methods based on non-Newtonian calculus is self-evident. In this paper, the well-known Runge-Kutta method for ordinary differential equations is developed in the frameworks of non-Newtonian calculus given in generalized form and then tested for different generating functions. The efficiency of the proposed non-Newtonian Euler and Runge-Kutta methods is exposed by examples, and the results are compared with the exact solutions.http://dx.doi.org/10.1155/2015/594685 |
| spellingShingle | Uğur Kadak Muharrem Özlük Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus Abstract and Applied Analysis |
| title | Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus |
| title_full | Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus |
| title_fullStr | Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus |
| title_full_unstemmed | Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus |
| title_short | Generalized Runge-Kutta Method with respect to the Non-Newtonian Calculus |
| title_sort | generalized runge kutta method with respect to the non newtonian calculus |
| url | http://dx.doi.org/10.1155/2015/594685 |
| work_keys_str_mv | AT ugurkadak generalizedrungekuttamethodwithrespecttothenonnewtoniancalculus AT muharremozluk generalizedrungekuttamethodwithrespecttothenonnewtoniancalculus |