New Iterative Method of Solving Nonlinear Equations in Fluid Mechanics

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.

Justification for the culverts’ design with joint operation of a water cylinder with a side weir

“…It is worth highlighting that a lateral weir is a weir made in the side wall of a water cylinder. The longitudinal flow of water is directed along the axis parallel to the weir crest in the cylinder [11]. The topics of solving the problem of excess flow energy dissipation, its interface with the bottom reach, open and closed culverts, and the reduction of erosion behind the end sections, do not lose its importance.…”