Phase-fitted and amplification-fitted higher order two-derivative Runge-Kutta method for the numerical solution of orbital and related periodical IVPs
A phase-fitted and amplification-fitted two-derivative Runge-Kutta (PFAFTDRK) method of high algebraic order for the numerical solution of first-order Initial Value Problems (IVPs) which possesses oscillatory solutions is derived. We present a sixth-order four-stage two-derivative Runge-Kutta (TDRK)...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2017
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/51859/ http://psasir.upm.edu.my/id/eprint/51859/1/51859.pdf |
| _version_ | 1848851947721850880 |
|---|---|
| author | Ahmad, Nur Amirah Senu, Norazak Ismail, Fudziah |
| author_facet | Ahmad, Nur Amirah Senu, Norazak Ismail, Fudziah |
| author_sort | Ahmad, Nur Amirah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A phase-fitted and amplification-fitted two-derivative Runge-Kutta (PFAFTDRK) method of high algebraic order for the numerical solution of first-order Initial Value Problems (IVPs) which possesses oscillatory solutions is derived. We present a sixth-order four-stage two-derivative Runge-Kutta (TDRK) method designed using the phase-fitted and amplification-fitted property. The stability of the new method is analyzed. The numerical experiments are carried out to show the efficiency of the derived methods in comparison with other existing Runge-Kutta (RK) methods. |
| first_indexed | 2025-11-15T10:30:17Z |
| format | Article |
| id | upm-51859 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:30:17Z |
| publishDate | 2017 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-518592017-05-02T08:05:20Z http://psasir.upm.edu.my/id/eprint/51859/ Phase-fitted and amplification-fitted higher order two-derivative Runge-Kutta method for the numerical solution of orbital and related periodical IVPs Ahmad, Nur Amirah Senu, Norazak Ismail, Fudziah A phase-fitted and amplification-fitted two-derivative Runge-Kutta (PFAFTDRK) method of high algebraic order for the numerical solution of first-order Initial Value Problems (IVPs) which possesses oscillatory solutions is derived. We present a sixth-order four-stage two-derivative Runge-Kutta (TDRK) method designed using the phase-fitted and amplification-fitted property. The stability of the new method is analyzed. The numerical experiments are carried out to show the efficiency of the derived methods in comparison with other existing Runge-Kutta (RK) methods. Hindawi Publishing Corporation 2017 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/51859/1/51859.pdf Ahmad, Nur Amirah and Senu, Norazak and Ismail, Fudziah (2017) Phase-fitted and amplification-fitted higher order two-derivative Runge-Kutta method for the numerical solution of orbital and related periodical IVPs. Mathematical Problems in Engineering, 2017. art. no. 1871278. pp. 1-11. ISSN 1024-123X; ESSN: 1563-5147 https://www.hindawi.com/journals/mpe/2017/1871278/abs/ 10.1155/2017/1871278 |
| spellingShingle | Ahmad, Nur Amirah Senu, Norazak Ismail, Fudziah Phase-fitted and amplification-fitted higher order two-derivative Runge-Kutta method for the numerical solution of orbital and related periodical IVPs |
| title | Phase-fitted and amplification-fitted higher order two-derivative Runge-Kutta method for the numerical solution of orbital and related periodical IVPs |
| title_full | Phase-fitted and amplification-fitted higher order two-derivative Runge-Kutta method for the numerical solution of orbital and related periodical IVPs |
| title_fullStr | Phase-fitted and amplification-fitted higher order two-derivative Runge-Kutta method for the numerical solution of orbital and related periodical IVPs |
| title_full_unstemmed | Phase-fitted and amplification-fitted higher order two-derivative Runge-Kutta method for the numerical solution of orbital and related periodical IVPs |
| title_short | Phase-fitted and amplification-fitted higher order two-derivative Runge-Kutta method for the numerical solution of orbital and related periodical IVPs |
| title_sort | phase-fitted and amplification-fitted higher order two-derivative runge-kutta method for the numerical solution of orbital and related periodical ivps |
| url | http://psasir.upm.edu.my/id/eprint/51859/ http://psasir.upm.edu.my/id/eprint/51859/ http://psasir.upm.edu.my/id/eprint/51859/ http://psasir.upm.edu.my/id/eprint/51859/1/51859.pdf |