New iterative method of solving nonlinear equations in fluid mechanics

• Autorzy: Palivets M. , Andreev E. , Bakshtanin A. , Benin D. , Snezhko V.

Identyfikatory

DOI

10.2478/ijame-2021-0042

• Języki publikacji: EN

Abstrakty

EN

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 01<α≤ or 12<α≤. 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.

Słowa kluczowe

EN

Adomian Decomposition Method ADM; earthquake; filtration; fluid mechanics; iterative method; nonlinear fractional partial differential equations; porous medium

PL

trzęsienie ziemi; mechanika płynów; porowatość

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2021
• Tom: Vol. 26, no. 3
• Strony: 163--176
• Opis fizyczny: Bibliogr. 33 poz..

Twórcy

autor

Palivets M.

• Department of Information Technology in the Agro-Industrial Complex Russian State Agrarian University - Moscow Timiryazev Agricultural Academy, Moscow, RUSSIA

autor

Andreev E.

• Department of Agricultural Construction and Real Estate Expertise, Russian State Agrarian University - Moscow Timiryazev Agricultural Academy, Moscow, RUSSIA

autor

Bakshtanin A.

• Department of Integrated Water Management and Hydraulics, Russian State Agrarian University - Moscow Timiryazev Agricultural Academy, Moscow, RUSSIA

autor

Benin D.

• Department of Information Technology in the Agro-Industrial Complex, Russian State Agrarian University - Moscow Timiryazev Agricultural Academy, Moscow, RUSSIA

autor

Snezhko V.

• Department of Information Technology in the Agro-Industrial Complex, Russian State Agrarian University - Moscow Timiryazev Agricultural Academy, Moscow, RUSSIA

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