Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation
作者： Songxin Liang , David J. Jeffrey
DOI: 10.1016/J.CNSNS.2009.02.016
关键词: n-connected 、 Series (mathematics) 、 Mathematics 、 Homotopy analysis method 、 Convergence (routing) 、 Symbolic computation 、 Convergent series 、 Exact solutions in general relativity 、 Mathematical analysis 、 Partial differential equation 、 Modelling and Simulation 、 Applied mathematics 、 Numerical analysis
摘要: In this paper, the homotopy analysis method (HAM) proposed by Liao in 1992 and perturbation (HPM) He 1998 are compared through an evolution equation used as second example a recent paper Ganji et al (2007). It is found that HPM special case of HAM when ~ = i1. However, solution divergent for all x t except 0. also given variational iteration (VIM) too. On other hand, using HAM, one obtains convergent series solutions which agree well with exact solution. This illustrates it very important to investigate convergence approximation series. Otherwise, might get useless results.
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