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The homotopy analysis method for solving the Fornberg–Whitham equation and comparison with Adomian’s decomposition method

✍ Scribed by Fayçal Abidi; Khaled Omrani

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
411 KB
Volume
59
Category
Article
ISSN
0898-1221

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✦ Synopsis

In this work, an analytical technique, namely the homotopy analysis method (HAM), is applied to obtain an approximate analytical solution of the Fornberg-Whitham equation. A comparison is made between the HAM results and the Adomian's decomposition method (ADM) and the homotopy perturbation method (HPM). The results reveal that HAM is very simple and effective. The HAM contains the auxiliary parameter h, which provides us with a simple way to adjust and control the convergence region of solution series.

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This paper compares the homotopy perturbation method with the sine-cosine wavelet method for solving linear integrodifferential equations. From the computational viewpoint, the homotopy perturbation method is more efficient and easier than the sine-cosine wavelet method.