Homotopy Analysis Method for Solving (2+1)-Dimensional Navier-Stokes Equations with Perturbation Terms (Communications in Mathematical Research, 2020)
In this paper Homotopy Analysis Method (HAM) is implemented forobtaining approximate solutions of (2+1)-dimensional Navier-Stokes equations withperturbation terms. The initial approximations are obtained using linear systems ofthe Navier-Stokes equations; by the iterations formula of HAM, the first approximation solutions and the second approximation solutions are successively obtained andHomotopy Perturbation Method (HPM) is also used to solve these equations; finally,approximate solutions by HAM of (2+1)-dimensional Navier-Stokes equations without perturbation terms and with perturbation terms are compared. Because of thefreedom of choice the auxiliary parameter of HAM, the results demonstrate that therapid convergence and the high accuracy of the HAM in solving Navier-Stokes equations; due to the effects of perturbation terms, the 3rd-order approximation solutionsby HAM and HPM have great fluctuation.