Sains Malaysiana 41(4)(2012): 489-492

Numerical Solution of First Order Stiff Ordinary Differential Equations using

Fifth Order Block Backward Differentiation Formulas

(Penyelesaian Berangka bagi Persamaan Pembezaan Biasa Kaku Peringkat

Satu Menggunakan Blok Formula Beza ke Belakang Peringkat Lima)

Nor Ain Azeany Mohd Nasir¹*, Zarina Bibi Ibrahim¹*, Khairil Iskandar Othman² & Mohamed Suleiman¹

¹Department of Mathematics, Faculty of Science, Universiti Putra Malaysia

43400 UPM Serdang, Selangor D.E. Malaysia

²Department of Mathematics, Faculty of Computer and Mathematical Sciences

Universiti Teknologi MARA, 40450 Shah Alam, Selangor D.E. Malaysia

Diserahkan: 4 Ogos 2010 / Diterima: 7 Oktober 2011

ABSTRACT

This paper describes the development of a two-point implicit code in the form of fifth order Block Backward Differentiation Formulas (BBDF(5)) for solving first order stiff Ordinary Differential Equations (ODEs). This method computes the approximate solutions at two points simultaneously within an equidistant block were computed. Numerical results are presented to compare the efficiency of the developed BBDF(5) to the classical one-point Backward Differentiation Formulas (BDF). The results indicated that the BBDF(5) outperformed the BDF in terms of total number of steps, accuracy and computational time.

Keywords: Block method; ordinary differential equation

ABSTRAK

Kertas ini membincangkan pembentukan kod tersirat dua titik dalam bentuk Blok Formula Beza Ke Belakang peringkat lima (BBDF(5)) bagi menyelesaikan Persamaan Pembezaan Biasa (PPB) kaku peringkat pertama. Kaedah ini mengira penyelesaian penghampiran dua titik serentak dalam jarak blok yang sama. Keputusan berangka diberi untuk membandingkan kaedah BBDF(5) dengan kaedah Formula Beza Ke Belakang klasik (BDF). Keputusan kajian menunjukkan bahawa BBDF(5) mengatasi BDF dalam hal jumlah langkah, kesalahan maksima dan masa pengkomputeraan.

Kata kunci: Kaedah blok; persamaan pembezaan biasa

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*Pengarang untuk surat-menyurat; email: zarina@math.upm.edu.my