Sains Malaysiana 41(11)(2012): 1489–1493
A Novel Computing Approach for Third
Order Boundary Layer Equation
(Kaedah Pengiraan Baru bagi Persamaan Lapisan Sempadan Tertib Ketiga)
Yasir Khan*
Department of
Mathematics, Zhejiang University, Hangzhou 310027, China
Zdeněk Smarda
Department of
Mathematics, Faculty of Electrical Engineering and Communication
Brno University of
Technology, Technicka 8, 61600 Brno Czech Republic
Diserahkan: 15 Jun 2012 / Diterima:
15 Julai 2012
ABSTRACT
This paper proposed an efficient
modification of homotopy perturbation
transform method (HPTM),
namely modified homotopy perturbation transform
method (MHPTM) for the solution of
third order boundary layer equation on semi-infinite domain. The technique was
based on the application of Laplace transform to boundary layers in fluid
mechanics. The nonlinear terms can be easily handled by the use of He’s
polynomials. The Pade´ approximants, that often show
superior performance over series approximations, were effectively used in the
analysis to capture the essential behavior of the boundary layer equation on
infinity. We then conduct a comparative study between the MHPTM and the existing results with the help of third order boundary
layer equation. The results obtained indicated that the MHPTM was effective and promising.
Keywords: He’s polynomials; modified Adomian decomposition method (MADM);
modified Laplace decomposition method (MLDM); Pade´ approximants; third order boundary layer
equation
ABSTRAK
Makalah ini mencadangkan pengubahsuaian yang lebih cekap untuk kaedah jelmaan usikan homotopi (HPTM), iaitu kaedah jelmaan usikan homotopi terubah suai (MHPTM) untuk menyelesaikan persamaan lapisan sempadan peringkat tiga dalam domain semi-terhingga. Teknik ini adalah berasaskan penggunaan jelmaan Laplace bagi lapisan sempadan dalam mekanik bendalir. Sebutan tak linear boleh ditangani dengan mudah menggunakan polinomial He. Penghampiran Padé yang sentiasa menunjukkan prestasi yang baik terhadap penghampiran-penghampiran siri digunakan secara cekap dalam analisis untuk memperoleh telatah penting persamaan lapisan sempadan di ketakterhinggaan. Kajian bandingan antara MHPTM dengan keputusan sedia ada dengan bantuan persamaan lapisan sempadan peringkat tiga juga dilakukan. Keputusan yang diperoleh menunjukkan yang MHPTM adalah berkesan dan meyakinkan.
Kata kunci: Kaedah penguraian Adomian terubah suai (MADM); kaedah penguraian Laplace terubah suai (MLDM); penghampiran Padé; persamaan lapisan sempadan peringkat tiga; polinomial He
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*Pengarang untuk surat-menyurat; email: yasirmath@yahoo.com
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