AIMS Mathematics (Feb 2024)

An analytical approach of multi-dimensional Navier-Stokes equation in the framework of natural transform

  • Manoj Singh,
  • Ahmed Hussein , Msmali,
  • Mohammad Tamsir ,
  • Abdullah Ali H. Ahmadini

DOI
https://doi.org/10.3934/math.2024426
Journal volume & issue
Vol. 9, no. 4
pp. 8776 – 8802

Abstract

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This article introduces a new iterative transform method and homotopy perturbation transform method along with a natural transform to analyze the multi-dimensional Navier-Stokes equations. To solve the fractional-derivative, the Caputo-Fabrizio definition of the fractional derivative was employed. Four examples were considered to examine the efficacy and accuracy of the proposed methods. The efficiency and accuracy were also demonstrated by the solution comparison via graphs. The proposed methods' convergence and uniqueness are also discussed. The methods mentioned above are straightforward and support a high rate of convergence.

Keywords