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Basic ideas of the homotopy analysis method

Basic ideas of the homotopy analysis method. Shijun LIAO Dept of Math., UCF , April 2007. Consider the nonlinear differential equation:. High-order deformation equation. High-order deformation equation. Choice of auxiliary linear operator. Choice of auxiliary linear operator.

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Basic ideas of the homotopy analysis method

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  1. Basic ideas of the homotopy analysis method Shijun LIAO Dept of Math., UCF , April 2007

  2. Consider the nonlinear differential equation:

  3. High-order deformation equation

  4. High-order deformation equation

  5. Choice of auxiliary linear operator

  6. Choice of auxiliary linear operator

  7. Choice of auxiliary linear operator

  8. Equation for

  9. Choice of the auxiliary parameter

  10. Choice of the auxiliary parameter The 10th-order approximations

  11. Choice of the auxiliary parameter Get convergent series when Green line: 10th-order approximation given by Red line: exact solution

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