Sains Malaysiana 40(5)(2011): 515–519
A New Hybrid Non-standard Finite Difference-Adomian
Scheme for Solution of Nonlinear Equations
(Skim Hibrid Baru
Beza-terhingga Tak Piawai-Adomian bagi Penyelesaian Persamaan Tak Linear)
K. Moaddy & I. Hashim*
School of Mathematical Sciences , Universiti Kebangsaan Malaysia
43600 UKM Bangi Selangor D.E., Malaysia
A.K. Alomari
Department of Sciences, Faculty of Nursing and Science
Jerash Private University, 26150 Jerash, Jordan
S. Momani
Department of Mathematics, Faculty of Science
The University of Jordan, Amman 11942 , Jordan
Diserahkan: 20 Mei 2010 / Diterima: 7 Julai 2010
ABSTRACT
This research develops a
new non-standard scheme based on the Adomian decomposition method (ADM)
to solve nonlinear equations. The ADM was adopted to solve the
nonlinear differential equation resulting from the discretization of the
differential equation. The new scheme does not need to linearize or non-locally
linearize the nonlinear term of the differential equation. Two examples are
given to demonstrate the efficiency of this scheme.
Keywords: Adomian
decomposition method; Logistic equation; Lotka-Volterra system; non-standard
schemes
ABSTRAK
Penyelidikan ini
membangunkan satu skim tak piawai baru berdasarkan pada kaedah penguraian
Adomian (KPA) bagi menyelesaikan persamaan tak linear. KPA ini
diadaptasi untuk menyelesaikan persamaan tak linear yang terhasil daripada
pendiskretan persamaan terbitan. Skim baru ini tidak perlu melinearkan atau melinearkan
secara tak setempat sebutan tak linear persamaan terbitan itu. Dua contoh
diberi untuk medemonstrasikan keefisienan skim ini.
Kata kunci: Kaedah
penguraian Adomian; persamaan logistik; skim tak piawai; sistem Lotka-Volterra
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*Pengarang untuk
surat-menyurat; email: ishak_h@ukm.my
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