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.

In this paper, we present a hybrid method combining the reduced differential transform method (RDTM) and a resumption method based on Yang transform and Padé approximant to find analytical solutions for three test problems for the unsteady state two-dimensional convection-diffusion equation. The proposed method significantly improves the approximate solution series and broadens the convergence field of RDTM. The numerical results obtained are compared to RDTM and other results from previous works. The results show that the proposed method is very efficient and has high accuracy. The main advantage of the proposed method is that it is based on a few straightforward steps and does not generate secular terms or depend on a perturbation parameter. We also provided a powerful and attractive mathematical tool for solving linear and nonlinear equations.

In this paper, an analytic approximate method for solving the unsteady two-dimensional convection-diffusion equations is introduced. Also, the convergence of the approximate methods is analyzed. Three test examples are presented, two have exact and one has not exacted solutions. The results obtained show that these methods are powerful mathematical tools for solving linear and nonlinear partial differential equations, moreover, new analytic Taylor method (NATM), reduced differential transform method (RDTM), and homotopy perturbation method (HPM), are more accurate and have less CPU time than the other methods.