Al-Saif, A.S.J. and Harfash, A.J. (2018) A Comparison between the Reduced Differential Transform Method and Perturbation-Iteration Algorithm for Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations. Journal of Applied Mathematics and Physics, 6, 2518-2543.
https://doi.org/10.4236/jamp.2018.612211

has been cited by the following article:

• TITLE: A New Approach to Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations

  AUTHORS: Zinah Abdulkadhim Hasan, Abdul-Sattar J. Al-Saif

  KEYWORDS: Navier-Stokes Equations, RDTM, Yang Transform, Padé Approximation, Accuracy, Convergence Analysis

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.10, October 28, 2022

  ABSTRACT: This paper proposes a new approach that combines the reduced differential transform method (RDTM), a resummation method based on the Yang transform, and a Padé approximant to the kinetically reduced local Navier-Stokes equation to find approximate solutions to the problem of lid-driven square cavity flow. The new approach, called PYRDM, considerably improves the convergence rate of the truncated series solution of RDTM and also is based on a simple process that yields highly precise estimates. The numerical results achieved by this method are compared to earlier studies’ results. Our results indicate that this method is more efficient and precise in generating analytic solutions. Furthermore, it provides highly precise solutions with good convergence that is simple to apply for great Reynolds and low Mach numbers. Moreover, the new solution’ graphs demonstrate the new approach’s validity, usefulness, and necessity.