Sains Malaysiana 39(3)(2010):
495–504
Analytical
Solution for Cauchy Reaction-Diffusion Problems by Homotopy Perturbation Method
(Penyelesaian Beranalisis Bagi
Masalah Tindak Balas-resapan Cauchy dengan Kaedah Usikan Homotopi)
M.S.H. Chowdhury
Department of Science in
Engineering, Faculty of Engineering
International Islamic University
Malaysia 53100 Gombak, Kuala Lumpur, Malaysia
I. Hashim*
Centre for Modelling & Data
Analysis School of Mathematical Sciences
Universiti Kebangsaan Malaysia 43600
Bangi, Selangor D. E., Malaysia
Diserahkan: 18 November 2008 / Diterima:
19 Oktober 2009
ABSTRACT
In this paper, the
homotopy-perturbation method (HPM) is
applied to obtain approximate analytical solutions for the Cauchy
reaction-diffusion problems. HPM yields
solutions in convergent series forms with easily computable terms. The HPM is tested for several examples.
Comparisons of the results obtained by the HPM with that obtained by the Adomian decomposition
method (ADM), homotopy
analysis method (HAM) and
the exact solutions show the efficiency of HPM.
Keywords: Cauchy problems;
Homotopy-perturbation method; reaction-diffusion equation
ABSTRAK
Dalam makalah ini, kaedah usikan
homotopi (KUH) diaplikasikan
bagi memperoleh penyelesaian hampiran beranalisis untuk masalah tindak
balas-resapan. KUH menghasilkan
penyelesaian dalam bentuk siri yang menumpu dengan sebutan mudah dihitung. KUH diuji terhadap beberapa contoh masalah.
Perbandingan keputusan yang diperoleh menerusi KUH dengan kaedah penguraian Adomian (KPA), kaedah homotopi analisis (KHA) dan penyelesaian tepat menunjukkan keefisienan KUH.
Kata kunci: Kaedah homotopi
usikan; masalah Cauchy; persamaan tindak balas-resapan
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*Pengarang untuk surat-menyurat;
email: ishak_h@ukm.my