In this paper, it is revealed that modified form of He's homotopy perturbation method corresponds to Adomian's decomposition method for certain nonlinear problems.
Adomian’s decomposition method and homotopy perturbation method in solving nonlinear equations
✍ Scribed by Jian-Lin Li
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 380 KB
- Volume
- 228
- Category
- Article
- ISSN
- 0377-0427
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✦ Synopsis
a b s t r a c t
The Adomian's decomposition method and the homotopy perturbation method are two powerful methods which consider the approximate solution of a nonlinear equation as an infinite series usually converging to the accurate solution. By theoretical analysis of the two methods, we show, in the present paper, that the two methods are equivalent in solving nonlinear equations.
📜 SIMILAR VOLUMES
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 (
In this paper, we conduct a comparative study among He's homotopy perturbation method and three traditional methods for an analytic and approximate treatment of nonlinear integral and integro-differential equations. The proper implementation of He's homotopy perturbation method can extremely minimiz