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

Received: 15 June 2012 / Accepted: 15 July 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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*Corresponding author; email: yasirmath@yahoo.com