Analytical Study of Navier-Stokes Equation with Fractional Orders Using He's Homotopy Perturbation and Variational Iteration Methods

Najeeb Alam Khan; Asmat Ara; Syed Anwer Ali; Amir Mahmood

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Analytical Study of Navier-Stokes Equation with Fractional Orders Using He's Homotopy Perturbation and Variational Iteration Methods

机译：利用He's同伦摄动和变分迭代方法对分数阶Navier-Stokes方程进行解析研究

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In the present work, by introducing the fractional derivative in the sense of Caputo, the He/s homotopy perturbation method (HPM) and variational iteration method (VIM) are used to study the Navier-Stokes equation with fractional orders. The analytical solutions are calculated in the form of series with easily computable components. Two examples are given. The present methods perform well in terms of efficiency and simplicity. A good agreement of the result is observed.

机译：在当前工作中，通过引入Caputo意义上的分数导数，使用He / s同伦扰动方法（HPM）和变分迭代方法（VIM）研究分数阶Navier-Stokes方程。分析解决方案以具有易于计算成分的级数形式进行计算。给出两个例子。本方法在效率和简单性方面表现良好。观察到结果的良好一致性。

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《International journal of nonlinear sciences and numerical simulation》 |2009年第9期|共8页
作者
Najeeb Alam Khan; Asmat Ara; Syed Anwer Ali; Amir Mahmood;
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原文格式 PDF
正文语种 eng
中图分类数值分析;
关键词
Fractional calculus; Navier-Stokes equation; Homotopy perturbation method (HPM); Variational iteration method (VIM);

机译：分数阶微积分;Navier-Stokes方程;同伦摄动法（HPM）;变分迭代法（VIM）;

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1. Analytical Study of Navier-Stokes Equation with Fractional Orders Using He's Homotopy Perturbation and Variational Iteration Methods [J] . Najeeb Alam Khan, Asmat Ara, Syed Anwer Ali, International journal of nonlinear sciences and numerical simulation . 2009,第9期

机译：利用He's同伦摄动和变分迭代方法对分数阶Navier-Stokes方程进行解析研究
2. Analytical investigation of beam deformation equation using perturbation, homotopy perturbation, variational iteration and optimal homotopy asymptotic methods [J] . Farrokhzad F, Mowlaee P, Barari A, Carpathian Journal of Mathematics . 2011,第1期

机译：使用摄动，同伦摄动，变分迭代和最优同伦渐近方法的梁变形方程的分析研究
3. Approximate Solution of Nonlinear fractional Integro-Di erential Equations By He's Homotopy Perturbation Method And The Modi cation of He's Variational Iteration Method [J] . M.H. Saleh, D.SH. Mohamed, M.H. Ahmed, Mathematical Theory and Modeling . 2015,第4期

机译：非线性分数阶微分积分微分方程的He's同伦摄动法和He's变分迭代法的近似解
4. An Approximate Analytical Solution of Fractional 2D Navier-Stokes Equation Using Homotopy-Perturbation Method [C] . N. Kumaresan, Kuru Ratnavelu National Symposium on Mathematical Sciences . 2015

机译：使用同型扰动法的分数2D Navier-Stokes方程的近似分析解决方法
5. A LAGRANGIAN FRACTIONAL STEP METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS (MULTIGRID). [D] . BORGERS, CHRISTOPH. 1985

机译：不可压Navier-Stokes方程（多重网格）的拉格朗日分数阶方法。
6. An approximate analytical solution of the Allen-Cahn equation using homotopy perturbation method and homotopy analysis method [O] . Safdar Hussain, Abdullah Shah, Sana Ayub, 2019

机译：同伦摄动法和同伦分析法对Allen-Cahn方程的近似解析解
7. Variational iteration method and homotopy perturbation method for fourth-order fractional integro-differential equations [O] . Nawaz Yasir 2011

机译：四阶分数阶积分-微分方程的变分迭代方法和同伦摄动方法

Analytical Study of Navier-Stokes Equation with Fractional Orders Using He's Homotopy Perturbation and Variational Iteration Methods

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