Sains Malaysiana 43(8)(2014): 1259-1262

A Third Order Nakashima Type Implicit Pseudo Runge-Kutta Method

for Delay Differential Equations

(Kaedah Runge-Kutta Nakashima Jenis 'Pseudo' Bertahap Tiga untuk Persamaan Perbezaan Lengah)

Lim Tian Hwee*

Foundation in Business, University of Reading Malaysia, Level 7, Menara Kotaraya, Jalan Trus
80000 Johor Bahru, Johor, Malaysia

Diserahkan: 24 Julai 2012/Diterima: 6 November 2013

ABSTRACT

A third order Nakashima type implicit Pseudo Runge-Kutta method is presented. The free parameter was determined by minimizing the error bound. The stability region of the method was presented. Some problems on delay differential equations are tested to compare the accuracy of the proposed method with third order RADAU I.

Keywords: Delay differential equations; implicit pseudo Runge-Kutta method; third order

ABSTRAK

Satu kaedah Runge-Kutta Nakashima tersirat jenis “pseudo” bertahap tiga telah diterbitkan. Parameter bebas telah ditentukan dengan meminimumkan batas ralat. Rantau kestabilan kaedah tersebut juga dipersembahkan. Beberapa soalan persamaan pembezaan lengah telah diuji untuk dibanding kejituan kaedah yang diteerbitkan dengan RADAU I bertahab tiga.

Kata kunci: Bertahap tiga; kaedah Runge-Kutta jenis 'pseudo' tersirat; persamaan perbezaan lengah

RUJUKAN

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Lotkin, M. 1951. On the accuracy of Runge-Kutta methods. Mathematical Tables and Other Aids to Computation 5(35): 128-133.

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Yaacob, N., Sabri, A.A., Samsudin, N. & Lim, T.H. 2011. Application of Nakashima's 2 stages 4^thorder Pseudo-Runge-Kutta method and 3 stages 5^th order Pseudo-Runge-Kutta Method to Delay Problems. UTM Technical Report, LT/M BIL.6/2011.

*Pengarang untuk surat-menyurat; email: t.h.lim@reading.ac.uk