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

Received: 18 November 2008 / Accepted: 19 October 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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*Corresponding author; email: ishak_h@ukm.my