Sains Malaysiana 50(6)(2021): 1799-1814

http://doi.org/10.17576/jsm-2021-5006-25

 

Numerical Study on Phase-Fitted and Amplification-Fitted Diagonally Implicit Two Derivative Runge-Kutta Method for Periodic IVPs

(Kajian Berangka ke atas Suai-Fasa dan Suai-Pembesaran Pepenjuru Tersirat Kaedah Runge-Kutta untuk MNA Berkala)

 

NORAZAK SENU1,2, NUR AMIRAH AHMAD1*, ZARINA BIBI IBRAHIM1,2 & MOHAMED OTHMAN1,3

 

1Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia

 

2Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia

 

3Department of Communication Technology and Network, Faculty of Computer Science and Information Technology, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia

 

Diserahkan: 26 Jun 2020/Diterima: 27 Oktober 2020

 

ABSTRACT

A fourth-order two stage Phase-fitted and Amplification-fitted Diagonally Implicit Two Derivative Runge-Kutta method (PFAFDITDRK) for the numerical integration of first-order Initial Value Problems (IVPs) which exhibits periodic solutions are constructed. The Phase-Fitted and Amplification-Fitted property are discussed thoroughly in this paper. The stability of the method proposed are also given herewith. Runge-Kutta (RK) methods of the similar property are chosen in the literature for the purpose of comparison by carrying out numerical experiments to justify the accuracy and the effectiveness of the derived method.

 

Keywords: Diagonally implicit methods; initial values problems; ordinary differential equations; phase-fitted and amplification-fitted; stability region; two derivative Runge-Kutta method

 

ABSTRAK

Kaedah Runge-Kutta Dua Terbitan Pepenjuru Tersirat Suai-Fasa dan Suai-Pembesaran (RKDTPTSFSP) tahap dua peringkat empat untuk penyelesaian pengamiran berangka Masalah Nilai Awal (MNA) peringkat pertama yang mengandungi penyelesaian berkala dibina. Sifat suai-fasa dan suai-pembesaran dibincangkan secara menyeluruh dalam kertas kajian ini. Kestabilan kaedah yang dicadangkan adalah seperti berikut. Kaedah Runge-Kutta (RK) dengan sifat yang sama dipilih di dalam kajian sorotan untuk tujuan perbandingan dengan menjalankan uji kaji berangka untuk memastikan kejituan dan keberkesanan kaedah yang diterbitkan.

 

Kata kunci: Kaedah pepenjuru tersirat; kaedah Runge-Kutta dua terbitan; masalah nilai awal; persamaan pembezaan biasa; rantau kestabilan; suai-fasa dan suai-pembesaran

 

RUJUKAN

Adel, F., Senu, N., Ismail, F. & Majid, Z.A. 2016. New efficient phase-fitted and amplification-fitted Runge-Kutta method for oscillatory problems. International Journal of Pure and Applied Mathematics 107(1): 69-86.

Ahmad, N.A., Senu, N. & Ismail, F. 2016. Phase-fitted and amplification-fitted diagonally implicit Runge-Kutta method for the numerical solution of periodic problems. Asian Journal of Mathematics and Computer Research 12(4): 252-264.