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Relationship to Euler Transform

In: Homotopy Analysis Method in Nonlinear Differential Equations

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  • Shijun Liao

    (Shanghai Jiao Tong University)

Abstract

The so-called generalized Taylor series and homotopy-transform are derived in the frame of the homotopy analysis method (HAM). Some related theorems are proved, which reveal in theory the reason why convergence-control parameter provides us a convenient way to guarantee the convergence of the homotopy-series solution. Especially, it is proved that the homotopy-transform logically contains the famous Euler transform that is often used to accelerate convergence of a series or to make a divergent series convergent. All of these provide us a conner-stone for the concept of convergence-control and the great generality of the HAM.

Suggested Citation

  • Shijun Liao, 2012. "Relationship to Euler Transform," Springer Books, in: Homotopy Analysis Method in Nonlinear Differential Equations, chapter 0, pages 189-221, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-25132-0_5
    DOI: 10.1007/978-3-642-25132-0_5
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