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
Diserahkan: 7 April 2015/Diterima: 5 Januari 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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*Pengarang untuk surat-menyurat: zarinabb@upm.edu.my
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