Volume 34, Issue 1
Homotopy Analysis Method for Solving (2+1)-Dimensional Navier-Stokes Equations with Perturbation Terms

Juanjuan Ji & Lanfang Zhang

Commun. Math. Res., 34 (2018), pp. 1-14.

Published online: 2019-12

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  • Abstract

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.

  • Keywords

Navier-Stokes equation, homotopy analysis method, homotopy perturbation method, perturbation term

  • AMS Subject Headings

35A35, 35B20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jjj0721@126.com (Juanjuan Ji)

  • BibTex
  • RIS
  • TXT
@Article{CMR-34-1, author = {Ji , Juanjuan and Zhang , Lanfang}, title = {Homotopy Analysis Method for Solving (2+1)-Dimensional Navier-Stokes Equations with Perturbation Terms}, journal = {Communications in Mathematical Research }, year = {2019}, volume = {34}, number = {1}, pages = {1--14}, abstract = {

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.

}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2018.01.01}, url = {http://global-sci.org/intro/article_detail/cmr/13468.html} }
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 -

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.

Juanjuan Ji & Lanfang Zhang. (2019). Homotopy Analysis Method for Solving (2+1)-Dimensional Navier-Stokes Equations with Perturbation Terms. Communications in Mathematical Research . 34 (1). 1-14. doi:10.13447/j.1674-5647.2018.01.01
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