Sains Malaysiana 42(6)(2013): 863–867

Application of Optimal Homotopy Asymptotic Method for the Approximate Solution

of Riccati Equation

(Pengunaan Kaedah Homotopi Asimptotik Optimum untuk Penyelesaian Hampiran Persamaan Riccati)

Fazle Mabood & Ahmad Izani bin Md Ismail

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang

Malaysia

Ishak Hashim*

School of Mathematical Sciences, Universiti Kebangsaan Malaysia

43600 Bangi, Selangor, Malaysia

Diserahkan: 18 Mei 2012/Diterima: 13 September 2012

ABSTRACT

In this paper, the optimal homotopy asymptotic method (OHAM) is applied to obtain an approximate solution of the nonlinear Riccati differential equation. The method is tested on several types of Riccati differential equations and comparisons that were made with numerical results showed the effectiveness and accuracy of this method.

Keywords: Optimal homotopy asymptotic method; Riccati differential equation

ABSTRAK

Dalam kertas ini, kaedah homotopi asimtotik optimum (OHAM) diaplikasi untuk memperoleh penyelesaian persamaan pembezaan Riccati tak linear. Kaedah ini diuji ke atas beberapa persamaan pembezaan Riccati dan perbandingan keputusan berangka menunjukkan keberkesanan dan kejituan kaedah ini.

Kata kunci: Kaedah homotopi asimptotik optimum; persamaan pembezaan Riccati

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*Pengarang untuk surat-menyurat; email: ishak_h@ukm.my