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S. Liao, “Notes on the Homotopy Analysis Method: Some Definitions and Theorems,” Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 4, 2009, pp. 983-997. doi:10.1016/j.cnsns.2008.04.013

has been cited by the following article:

• TITLE: A Modified Homotopy Analysis Method for Solving Boundary Layer Equations

  AUTHORS: Yinlong Zhao, Zhiliang Lin, Shijun Liao

  KEYWORDS: Homotopy Analysis Method; Boundary Layer Equations; Orthonormal Functions

  JOURNAL NAME: Applied Mathematics, Vol.4 No.1, January 25, 2013

  ABSTRACT: A new modification of the Homotopy Analysis Method (HAM) is presented for highly nonlinear ODEs on a semi-infinite domain. The main advantage of the modified HAM is that the number of terms in the series solution can be greatly reduced; meanwhile the accuracy of the solution can be well retained. In this way, much less CPU is needed. Two typical examples are used to illustrate the efficiency of the proposed approach.