Hybrid methods for solving special fourth order ordinary differential equations
In recent time, Runge-Kutta methods that integrate special fourth or- der ordinary differential equations (ODEs) directly are proposed to ad- dress efficiency issues associated with classical Runge-Kutta methods. Although, the methods require approximation of y′, y′′ and y′′′ of the solution at...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Institute for Mathematical Research, Universiti Putra Malaysia
2019
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| Online Access: | http://psasir.upm.edu.my/id/eprint/80109/ http://psasir.upm.edu.my/id/eprint/80109/1/3.pdf |
| _version_ | 1848858831253143552 |
|---|---|
| author | Jikantoro, Y. D. Ismail, F. Senu, N. Ibrahim, Z. B. Aliyu, Y. B. |
| author_facet | Jikantoro, Y. D. Ismail, F. Senu, N. Ibrahim, Z. B. Aliyu, Y. B. |
| author_sort | Jikantoro, Y. D. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In recent time, Runge-Kutta methods that integrate special fourth or-
der ordinary differential equations (ODEs) directly are proposed to ad-
dress efficiency issues associated with classical Runge-Kutta methods.
Although, the methods require approximation of y′, y′′ and y′′′ of the
solution at every step. In this paper, a hybrid type method is proposed,
which can directly integrate special fourth order ODEs. The method
does not require the approximation of any derivatives of the solution.
Algebraic order conditions of the methods are derived via Taylor series
technique. Using the order conditions, eight algebraic order method is
presented. Absolute stability of the method is analyzed and the stabil-
ity region presented. Numerical experiment is conducted on some test
problems. Results from the experiment show that the new method is
more efficient and accurate than the existing Runge-Kutta and hybrid
methods with similar number of function evaluation. |
| first_indexed | 2025-11-15T12:19:41Z |
| format | Article |
| id | upm-80109 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:19:41Z |
| publishDate | 2019 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-801092023-04-05T02:59:35Z http://psasir.upm.edu.my/id/eprint/80109/ Hybrid methods for solving special fourth order ordinary differential equations Jikantoro, Y. D. Ismail, F. Senu, N. Ibrahim, Z. B. Aliyu, Y. B. In recent time, Runge-Kutta methods that integrate special fourth or- der ordinary differential equations (ODEs) directly are proposed to ad- dress efficiency issues associated with classical Runge-Kutta methods. Although, the methods require approximation of y′, y′′ and y′′′ of the solution at every step. In this paper, a hybrid type method is proposed, which can directly integrate special fourth order ODEs. The method does not require the approximation of any derivatives of the solution. Algebraic order conditions of the methods are derived via Taylor series technique. Using the order conditions, eight algebraic order method is presented. Absolute stability of the method is analyzed and the stabil- ity region presented. Numerical experiment is conducted on some test problems. Results from the experiment show that the new method is more efficient and accurate than the existing Runge-Kutta and hybrid methods with similar number of function evaluation. Institute for Mathematical Research, Universiti Putra Malaysia 2019 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/80109/1/3.pdf Jikantoro, Y. D. and Ismail, F. and Senu, N. and Ibrahim, Z. B. and Aliyu, Y. B. (2019) Hybrid methods for solving special fourth order ordinary differential equations. Malaysian Journal of Mathematical Sciences, 13 (spec.). pp. 27-40. ISSN 1823-8343; ESSN: 2289-750X https://einspem.upm.edu.my/journal/fullpaper/vol13sapril/3.pdf |
| spellingShingle | Jikantoro, Y. D. Ismail, F. Senu, N. Ibrahim, Z. B. Aliyu, Y. B. Hybrid methods for solving special fourth order ordinary differential equations |
| title | Hybrid methods for solving special fourth order ordinary differential equations |
| title_full | Hybrid methods for solving special fourth order ordinary differential equations |
| title_fullStr | Hybrid methods for solving special fourth order ordinary differential equations |
| title_full_unstemmed | Hybrid methods for solving special fourth order ordinary differential equations |
| title_short | Hybrid methods for solving special fourth order ordinary differential equations |
| title_sort | hybrid methods for solving special fourth order ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/80109/ http://psasir.upm.edu.my/id/eprint/80109/ http://psasir.upm.edu.my/id/eprint/80109/1/3.pdf |