Sains Malaysiana 45(6)(2016): 989–998

Block Backward Differentiation Formulas for Solving First Order Fuzzy Differential Equations under Generalized Differentiability

(Formula Blok Pembezaan Kebelakang bagi Menyelesaikan Persamaan Pembezaan Kabur Peringkat Pertama di bawah Kebolehbezaan Umum)

ISKANDAR SHAH MOHD ZAWAWI¹ & ZARINA BIBI IBRAHIM²*

¹Department of Mathematicsm Faculty of Sciencem Universiti Putra Malaysia, 43400 Serdang, Selangor Darul Ehsan, Malaysia

²Institute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor Darul Ehsan, Malaysia

Received: 7 April 2015/Accepted: 5 January 2015

ABSTRACT

In this paper, the fully implicit 2-point block backward differentiation formula and diagonally implicit 2-point block backward differentiation formula were developed under the interpretation of generalized differentiability concept for solving first order fuzzy differential equations. Some fuzzy initial value problems were tested in order to demonstrate the performance of the developed methods. The approximated solutions for both methods were in good agreement with the exact solutions. The numerical results showed that the diagonally implicit method outperforms the fully implicit method in term of accuracy.

Keywords: Block; diagonally; fuzzy; implicit

ABSTRAK

Dalam kertas ini, formula 2-titik blok pembezaan kebelakang tersirat penuh dan formula 2-titik blok pembezaan kebelakang tersirat pepenjuru dibangunkan di bawah konsep kebolehbezaan umum bagi menyelesaikan persamaan pembezaan kabur peringkat pertama. Beberapa masalah-masalah nilai awal kabur diuji untuk menunjukkan prestasi kaedah yang dibangunkan. Penyelesaian yang dianggarkan bagi kedua-dua kaedah adalah dalam persetujuan yang baik dengan penyelesaian tepat. Keputusan berangka menunjukkan kaedah tersirat pepenjuru mengatasi kaedah tersirat penuh dalam terma kejituan.

Kata kunci: Blok; kabur; pepenjuru; tersirat

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*Corresponding author: zarinabb@upm.edu.my