The present work is devoted to using an analytic approach, namely the homotopy analysis method, to obtain convergent series solutions of strongly nonlinear problems. On the basis of the homotopy derivative concept described in Liao (2009) [3], a theorem is proved here which generalizes some lemmas a
Notes on the homotopy analysis method: Some definitions and theorems
β Scribed by Shijun Liao
- Book ID
- 108096853
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 284 KB
- Volume
- 14
- Category
- Article
- ISSN
- 1007-5704
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π SIMILAR VOLUMES
A new transform, namely the homotopy transform, is defined for the first time. Then, it is proved that the famous Euler transform is only a special case of the so-called homotopy transform which depends upon one non-zero auxiliary parameter h and two convergent series P ΓΎ1 kΒΌ1 a 1;k ΒΌ 1 and In the
In this paper, by means of the homotopy analysis method (HAM), the solutions of some Schrodinger equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter h, that provides a convenient way of controlling the convergent region of series solutions
The "rst remark of this paper is to disclose a historical fact that the assumed stress hybrid "nite element method pioneered by Pian [1] in 1964 was actually developed originally based on the Hellinger}Reissner principle and not on the complementary energy principle as indicated in the published pap