Technical report: solving nonlinear equation by using Homotopy Analysis Method (HAM) / Nur Saadah Mohtar and Syarifah Nur Ainina Said Abdul Karim - Mohtar, Nur Saadah; Abdul Karim, Syarifah Nur Ainina Said (2018)
In this research, the Homotopy Analysis Method (HAM) was studied and had been employed to obtain the approximate analytical solution of non-linear of Couple-Burgers Equation and Pomberg-Whitman Equation. When applied to non-linear equation the numerical result revealed that this method was more accurate, reliable and easy to implement. This was because of some limitations that appeared in other methods. Some other perturbation methods could only be solved based on small convergence region and was only valid for small parameter. By using Homotopy Analysis Method (HAM) we could choose the auxiliary parameter so that the zero-order and higher-order deformation equation could be obtained. Then two examples which are Couple-Burger Equation and Pomberg-Whitham Equation were applied. The final result that was reported by HAM is compared with the exact solution and Adomian Decomposition Method (ADM). The solution then was graphed using Maple software. Corresponding to it, it was found that the Homotopy Analysis Method was more accurate and effective compare to Adomian Decomposition Method that obtained by previously published work for validation.