New Iterative Method of Solving Nonlinear Equations in Fluid Mechanics
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Department of Information Technology in the Agro-Industrial Complex, Russian State Agrarian University - Moscow Timiryazev Agricultural Academy, Moscow, Russia, E-mail: paliivetsmax@rambler.ru
Department of Agricultural Construction and Real Estate Expertise, Russian State Agrarian University - Moscow Timiryazev Agricultural Academy, Moscow, Russia
Department of Integrated Water Management and Hydraulics, Russian State Agrarian University - Moscow, Timiryazev Agricultural Academy, Moscow, Russia
Department of Information Technology in the Agro-Industrial Complex, Russian State Agrarian University - Moscow Timiryazev Agricultural Academy, Moscow, Russia
Online publication date: 2021-08-26
Publication date: 2021-09-01
International Journal of Applied Mechanics and Engineering 2021;26(3):163-176
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.
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