1. bookVolume 26 (2021): Issue 3 (September 2021)
Journal Details
License
Format
Journal
First Published
19 Apr 2013
Publication timeframe
4 times per year
Languages
English
access type Open Access

New Iterative Method of Solving Nonlinear Equations in Fluid Mechanics

Published Online: 26 Aug 2021
Page range: 163 - 176
Received: 23 Mar 2021
Accepted: 24 Jul 2021
Journal Details
License
Format
Journal
First Published
19 Apr 2013
Publication timeframe
4 times per year
Languages
English
Abstract

This paper presents the results of applying a new iterative method to linear and nonlinear fractional partial differential equations in fluid mechanics. A numerical analysis was performed to find an exact solution of the fractional wave equation and fractional Burgers’ equation, as well as an approximate solution of fractional KdV equation and fractional Boussinesq equation. Fractional derivatives of the order α are described using Caputo's definition with 0 < α ≤ 1 or 1 < α ≤ 2. A comparative analysis of the results obtained using a new iterative method with those obtained by the Adomian decomposition method showed the first method to be more efficient and simple, providing accurate results in fewer computational operations. Given its flexibility and ability to solve nonlinear equations, the iterative method can be used to solve more complex linear and nonlinear fractional partial differential equations.

Keywords

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