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Variational iteration method for Bratu-like equation arising in electrospinning.

Ji-Huan He1, Hai-Yan Kong2, Rou-Xi Chen2

  • 1National Engineering Laboratory for Modern Silk, College of Textile and Clothing Engineering, Soochow University, 199 Ren-ai Road, Suzhou 215123, China; Nantong Textile Institute, Soochow University, 58 Chong Chuan Road, Nantong, China.

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Summary

The enhanced variational iteration method for electrospinning is actually the standard method. A new algorithm using variational iteration algorithm-II effectively solves Bratu-like equations with few iterations.

Keywords:
Analytical solutionBubbfil spinningElectrospinningVariational iteration methodVibration-electrospinning

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Area of Science:

  • Applied Mathematics
  • Chemical Engineering
  • Materials Science

Background:

  • Nonlinear equations are central to modeling complex physical phenomena like electrospinning and its vibration-assisted variant.
  • The variational iteration method (VIM) is a powerful analytical technique for solving such equations.
  • Previous work proposed an 'enhanced' VIM, necessitating clarification and refinement.

Purpose of the Study:

  • To clarify the distinction between the standard VIM and the so-called enhanced VIM.
  • To propose an effective and efficient algorithm for solving Bratu-like equations relevant to electrospinning.
  • To demonstrate the accuracy and speed of the proposed method.

Main Methods:

  • Comparative analysis of the standard VIM and the purported enhanced VIM.
  • Development and application of the variational iteration algorithm-II.
  • Utilizing a carefully selected initial guess for rapid convergence.

Main Results:

  • The 'enhanced' VIM is demonstrated to be identical to the standard VIM.
  • The proposed variational iteration algorithm-II provides an effective solution for Bratu-like equations in electrospinning.
  • Accurate solutions are achieved with only one or a few iterations.

Conclusions:

  • The terminology 'enhanced VIM' in the context of electrospinning nonlinear equations is redundant.
  • The variational iteration algorithm-II offers a computationally efficient and accurate approach for electrospinning simulations.
  • This method significantly reduces the number of iterations required for convergence, saving computational resources.