A Comparison between the Reduced Differential Transform Method and Perturbation-Iteration Algorithm for Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations

Abstract

In this work, approximate analytical solutions to the lid-driven square cavity flow problem, which satisfied two-dimensional unsteady incompressible Navier-Stokes equations, are presented using the kinetically reduced local Navier-Stokes equations. Reduced differential transform method and perturbation-iteration algorithm are applied to solve this problem. The convergence analysis was discussed for both methods. The numerical results of both methods are given at some Reynolds numbers and low Mach numbers, and compared with results of earlier studies in the review of the literatures. These two methods are easy and fast to implement, and the results are close to each other and other numerical results, so it can be said that these methods are useful in finding approximate analytical solutions to the unsteady incompressible flow problems at low Mach numbers.

Approximate Analytic Solutions of Two-Dimensional Nonlinear Klein–Gordon Equation by Using the Reduced Differential Transform Method

“…irdly, this method can reduce the size of the calculations and can provide an analytic approximation, in many cases exact solutions, in rapidly convergent power series form with elegantly computed terms (see [29] and the references therein). Moreover, the reduced differential transform method (RDTM) has an alternative approach of solving problems to overcome the demerit of discretization, linearization, or perturbations of well-known numerical and analytical methods such as Adomian decomposition, differential transform, homotopy perturbation, and variational iteration [29,30]. e structure of the remaining parts of this paper is organized as follows.…”

On the wave solutions of time‐fractional Sawada‐Kotera‐Ito equation arising in shallow water

“…Also, one may see Al‐Saif and Harfash 45 for the convergence analysis of the present method theoretically.…”

“…So, the analytical result of Equation 23 is written as φ x, t ð Þ= lim n!∞ φ n x, t ð Þ. Also, one may see Al-Saif and Harfash 45 for the convergence analysis of the present method theoretically.…”

“…In this section, we will illustrate the necessary steps for the FRDTM. [41][42][43][44][45] First, let us consider a function of (n + 1) variables…”

“…In this section, we will illustrate the necessary steps for the FRDTM 41–45 . First, let us consider a function of ( n + 1) variables ϕ ( t , x 1 , x 2 , .., x n ) such that …”