TY - JOUR
T1 - Homotopy Analysis Method for Solving (2+1)-Dimensional Navier-Stokes Equations with Perturbation Terms
AU - Ji , Juanjuan
AU - Zhang , Lanfang
JO - Communications in Mathematical Research 
VL - 1
SP - 1
EP - 14
PY - 2019
DA - 2019/12
SN - 34
DO - http://doi.org/10.13447/j.1674-5647.2018.01.01
UR - https://global-sci.org/intro/article_detail/cmr/13468.html
KW - Navier-Stokes equation, homotopy analysis method, homotopy perturbation method, perturbation term
AB - <p style="text-align: justify;">In this paper Homotopy Analysis Method (HAM) is implemented for
obtaining approximate solutions of (2+1)-dimensional Navier-Stokes equations with
perturbation terms. The initial approximations are obtained using linear systems of
the Navier-Stokes equations; by the iterations formula of HAM, the first approximation solutions and the second approximation solutions are successively obtained and
Homotopy 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 the
freedom of choice the auxiliary parameter of HAM, the results demonstrate that the
rapid convergence and the high accuracy of the HAM in solving Navier-Stokes equations; due to the effects of perturbation terms, the 3rd-order approximation solutions
by HAM and HPM have great fluctuation.</p>