The Comparison Study of the Hybrid Method for Solving the Unsteady State Two-Dimensional Convection-Diffusion Equations

Abstract

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.